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* gsl-ref: (gsl-ref).                   GNU Scientific Library - Reference
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   Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004,
2005, 2006, 2007, 2008, 2009, 2010, 2011 The GSL Team.

   Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
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Invariant Sections being "GNU General Public License" and "Free Software
Needs Free Documentation", the Front-Cover text being "A GNU Manual",
and with the Back-Cover Text being (a) (see below).  A copy of the
license is included in the section entitled "GNU Free Documentation
License".

   (a) The Back-Cover Text is: "You have the freedom to copy and modify
this GNU Manual."


File: gsl-ref.info,  Node: Concept Index,  Prev: Type Index,  Up: Top

Concept Index
*************

 [index ]
* Menu:

* $, shell prompt:                       Conventions used in this manual.
                                                              (line   6)
* 2D histograms:                         Two dimensional histograms.
                                                              (line   6)
* 2D random direction vector:            Spherical Vector Distributions.
                                                              (line  14)
* 3-j symbols:                           Coupling Coefficients.
                                                              (line   6)
* 3D random direction vector:            Spherical Vector Distributions.
                                                              (line  33)
* 6-j symbols:                           Coupling Coefficients.
                                                              (line   6)
* 9-j symbols:                           Coupling Coefficients.
                                                              (line   6)
* acceleration of series:                Series Acceleration. (line   6)
* acosh:                                 Elementary Functions.
                                                              (line  33)
* Adams method:                          Stepping Functions.  (line 129)
* Adaptive step-size control, differential equations: Adaptive Step-size Control.
                                                              (line   6)
* Ai(x):                                 Airy Functions and Derivatives.
                                                              (line   6)
* Airy functions:                        Airy Functions and Derivatives.
                                                              (line   6)
* Akima splines:                         Interpolation Types. (line  36)
* aliasing of arrays:                    Aliasing of arrays.  (line   6)
* alternative optimized functions:       Alternative optimized functions.
                                                              (line   6)
* AMAX, Level-1 BLAS:                    Level 1 GSL BLAS Interface.
                                                              (line  62)
* Angular Mathieu Functions:             Angular Mathieu Functions.
                                                              (line   6)
* angular reduction:                     Restriction Functions.
                                                              (line   6)
* ANSI C, use of:                        Using the library.   (line   6)
* Apell symbol, see Pochhammer symbol:   Pochhammer Symbol.   (line   9)
* approximate comparison of floating point numbers: Approximate Comparison of Floating Point Numbers.
                                                              (line  13)
* arctangent integral:                   Arctangent Integral. (line   6)
* argument of complex number:            Properties of complex numbers.
                                                              (line   7)
* arithmetic exceptions:                 Setting up your IEEE environment.
                                                              (line   6)
* asinh:                                 Elementary Functions.
                                                              (line  37)
* astronomical constants:                Astronomy and Astrophysics.
                                                              (line   6)
* ASUM, Level-1 BLAS:                    Level 1 GSL BLAS Interface.
                                                              (line  47)
* atanh:                                 Elementary Functions.
                                                              (line  41)
* atomic physics, constants:             Atomic and Nuclear Physics.
                                                              (line   6)
* autoconf, using with GSL:              Autoconf Macros.     (line   6)
* AXPY, Level-1 BLAS:                    Level 1 GSL BLAS Interface.
                                                              (line  96)
* B-spline wavelets:                     DWT Initialization.  (line  31)
* Bader and Deuflhard, Bulirsch-Stoer method.: Stepping Functions.
                                                              (line 124)
* balancing matrices:                    Balancing.           (line   6)
* Basic Linear Algebra Subroutines (BLAS) <1>: GSL CBLAS Library.
                                                              (line   6)
* Basic Linear Algebra Subroutines (BLAS): BLAS Support.      (line   6)
* basis splines, B-splines:              Basis Splines.       (line   6)
* basis splines, derivatives:            Evaluation of B-spline basis function derivatives.
                                                              (line   6)
* basis splines, evaluation:             Evaluation of B-spline basis functions.
                                                              (line   6)
* basis splines, examples:               Example programs for B-splines.
                                                              (line   6)
* basis splines, Greville abscissae:     Obtaining Greville abscissae for B-spline basis functions.
                                                              (line   6)
* basis splines, initializing:           Initializing the B-splines solver.
                                                              (line   6)
* basis splines, overview:               Overview of B-splines.
                                                              (line   6)
* BDF method:                            Stepping Functions.  (line 137)
* Bernoulli trial, random variates:      The Bernoulli Distribution.
                                                              (line   8)
* Bessel functions:                      Bessel Functions.    (line   6)
* Bessel Functions, Fractional Order:    Regular Bessel Function - Fractional Order.
                                                              (line   6)
* best-fit parameters, covariance:       Computing the covariance matrix of best fit parameters.
                                                              (line   6)
* Beta distribution:                     The Beta Distribution.
                                                              (line   8)
* Beta function:                         Beta Functions.      (line   9)
* Beta function, incomplete normalized:  Incomplete Beta Function.
                                                              (line   9)
* BFGS algorithm, minimization:          Multimin Algorithms with Derivatives.
                                                              (line  37)
* Bi(x):                                 Airy Functions and Derivatives.
                                                              (line   6)
* bias, IEEE format:                     Representation of floating point numbers.
                                                              (line   6)
* bidiagonalization of real matrices:    Bidiagonalization.   (line   6)
* binning data:                          Histograms.          (line   6)
* Binomial random variates:              The Binomial Distribution.
                                                              (line   9)
* biorthogonal wavelets:                 DWT Initialization.  (line  31)
* bisection algorithm for finding roots: Root Bracketing Algorithms.
                                                              (line  17)
* Bivariate Gaussian distribution:       The Bivariate Gaussian Distribution.
                                                              (line   9)
* BLAS:                                  BLAS Support.        (line   6)
* BLAS, Low-level C interface:           GSL CBLAS Library.   (line   6)
* blocks:                                Vectors and Matrices.
                                                              (line   6)
* bounds checking, extension to GCC:     Accessing vector elements.
                                                              (line   6)
* breakpoints:                           Using gdb.           (line   6)
* Brent's method for finding minima:     Minimization Algorithms.
                                                              (line  32)
* Brent's method for finding roots:      Root Bracketing Algorithms.
                                                              (line  50)
* Broyden algorithm for multidimensional roots: Algorithms without Derivatives.
                                                              (line  45)
* BSD random number generator:           Unix random number generators.
                                                              (line  18)
* bug-gsl mailing list:                  Reporting Bugs.      (line   6)
* bugs, how to report:                   Reporting Bugs.      (line   6)
* Bulirsch-Stoer method:                 Stepping Functions.  (line 124)
* C extensions, compatible use of:       Using the library.   (line   6)
* C++, compatibility:                    Compatibility with C++.
                                                              (line   6)
* C99, inline keyword:                   Inline functions.    (line   6)
* Carlson forms of Elliptic integrals:   Definition of Carlson Forms.
                                                              (line   6)
* Cash-Karp, Runge-Kutta method:         Stepping Functions.  (line 100)
* Cauchy distribution:                   The Cauchy Distribution.
                                                              (line   7)
* Cauchy principal value, by numerical quadrature: QAWC adaptive integration for Cauchy principal values.
                                                              (line   6)
* CBLAS:                                 BLAS Support.        (line   6)
* CBLAS, Low-level interface:            GSL CBLAS Library.   (line   6)
* CDFs, cumulative distribution functions: Random Number Distributions.
                                                              (line   6)
* ce(q,x), Mathieu function:             Angular Mathieu Functions.
                                                              (line   6)
* Chebyshev series:                      Chebyshev Approximations.
                                                              (line   6)
* checking combination for validity:     Combination properties.
                                                              (line  18)
* checking multiset for validity:        Multiset properties. (line  17)
* checking permutation for validity:     Permutation properties.
                                                              (line  14)
* Chi(x):                                Hyperbolic Integrals.
                                                              (line   6)
* Chi-squared distribution:              The Chi-squared Distribution.
                                                              (line  15)
* Cholesky decomposition:                Cholesky Decomposition.
                                                              (line   6)
* Ci(x):                                 Trigonometric Integrals.
                                                              (line   6)
* Clausen functions:                     Clausen Functions.   (line   6)
* Clenshaw-Curtis quadrature:            Integrands with weight functions.
                                                              (line   6)
* CMRG, combined multiple recursive random number generator: Random number generator algorithms.
                                                              (line  97)
* code reuse in applications:            Code Reuse.          (line   6)
* combinations:                          Combinations.        (line   6)
* combinatorial factor C(m,n):           Factorials.          (line  42)
* combinatorial optimization:            Simulated Annealing. (line   6)
* comparison functions, definition:      Sorting objects.     (line  16)
* compatibility:                         Using the library.   (line   6)
* compiling programs, include paths:     Compiling and Linking.
                                                              (line   6)
* compiling programs, library paths:     Linking programs with the library.
                                                              (line   6)
* complementary incomplete Gamma function: Incomplete Gamma Functions.
                                                              (line  23)
* complete Fermi-Dirac integrals:        Complete Fermi-Dirac Integrals.
                                                              (line   6)
* complex arithmetic:                    Complex arithmetic operators.
                                                              (line   6)
* complex cosine function, special functions: Trigonometric Functions for Complex Arguments.
                                                              (line  13)
* Complex Gamma function:                Gamma Functions.     (line  56)
* complex hermitian matrix, eigensystem: Complex Hermitian Matrices.
                                                              (line   9)
* complex log sine function, special functions: Trigonometric Functions for Complex Arguments.
                                                              (line  18)
* complex numbers:                       Complex Numbers.     (line   6)
* complex sinc function, special functions: Circular Trigonometric Functions.
                                                              (line  22)
* complex sine function, special functions: Trigonometric Functions for Complex Arguments.
                                                              (line   8)
* confluent hypergeometric function:     Laguerre Functions.  (line   6)
* confluent hypergeometric functions:    Hypergeometric Functions.
                                                              (line   6)
* conical functions:                     Legendre Functions and Spherical Harmonics.
                                                              (line   6)
* Conjugate gradient algorithm, minimization: Multimin Algorithms with Derivatives.
                                                              (line  12)
* conjugate of complex number:           Complex arithmetic operators.
                                                              (line  55)
* constant matrix:                       Initializing matrix elements.
                                                              (line   6)
* constants, fundamental:                Fundamental Constants.
                                                              (line   6)
* constants, mathematical--defined as macros: Mathematical Constants.
                                                              (line   6)
* constants, physical:                   Physical Constants.  (line   6)
* constants, prefixes:                   Prefixes.            (line   6)
* contacting the GSL developers:         Further Information. (line   6)
* conventions, used in manual:           Conventions used in this manual.
                                                              (line   6)
* convergence, accelerating a series:    Series Acceleration. (line   6)
* conversion of units:                   Physical Constants.  (line   6)
* cooling schedule:                      Simulated Annealing algorithm.
                                                              (line  23)
* COPY, Level-1 BLAS:                    Level 1 GSL BLAS Interface.
                                                              (line  85)
* correlation, of two datasets:          Correlation.         (line   6)
* cosine function, special functions:    Circular Trigonometric Functions.
                                                              (line  12)
* cosine of complex number:              Complex Trigonometric Functions.
                                                              (line  11)
* cost function:                         Simulated Annealing. (line   6)
* Coulomb wave functions:                Coulomb Functions.   (line   6)
* coupling coefficients:                 Coupling Coefficients.
                                                              (line   6)
* covariance matrix, from linear regression: Linear regression.
                                                              (line   9)
* covariance matrix, linear fits:        Fitting Overview.    (line  21)
* covariance matrix, nonlinear fits:     Computing the covariance matrix of best fit parameters.
                                                              (line   6)
* covariance, of two datasets:           Covariance.          (line   6)
* cquad, doubly-adaptive integration:    CQUAD doubly-adaptive integration.
                                                              (line   6)
* CRAY random number generator, RANF:    Other random number generators.
                                                              (line  23)
* cubic equation, solving:               Cubic Equations.     (line   6)
* cubic splines:                         Interpolation Types. (line  20)
* cumulative distribution functions (CDFs): Random Number Distributions.
                                                              (line   6)
* Cylindrical Bessel Functions:          Regular Cylindrical Bessel Functions.
                                                              (line   6)
* Daubechies wavelets:                   DWT Initialization.  (line  20)
* Dawson function:                       Dawson Function.     (line   6)
* DAXPY, Level-1 BLAS:                   Level 1 GSL BLAS Interface.
                                                              (line  96)
* debugging numerical programs:          Using gdb.           (line   6)
* Debye functions:                       Debye Functions.     (line   6)
* denormalized form, IEEE format:        Representation of floating point numbers.
                                                              (line  14)
* deprecated functions:                  Deprecated Functions.
                                                              (line   6)
* derivatives, calculating numerically:  Numerical Differentiation.
                                                              (line   6)
* determinant of a matrix, by LU decomposition: LU Decomposition.
                                                              (line  83)
* Deuflhard and Bader, Bulirsch-Stoer method.: Stepping Functions.
                                                              (line 124)
* DFTs, see FFT:                         Fast Fourier Transforms.
                                                              (line   6)
* diagonal, of a matrix:                 Creating row and column views.
                                                              (line  62)
* differential equations, initial value problems: Ordinary Differential Equations.
                                                              (line   6)
* differentiation of functions, numeric: Numerical Differentiation.
                                                              (line   6)
* digamma function:                      Psi (Digamma) Function.
                                                              (line   6)
* dilogarithm:                           Dilogarithm.         (line   6)
* direction vector, random 2D:           Spherical Vector Distributions.
                                                              (line  14)
* direction vector, random 3D:           Spherical Vector Distributions.
                                                              (line  33)
* direction vector, random N-dimensional: Spherical Vector Distributions.
                                                              (line  42)
* Dirichlet distribution:                The Dirichlet Distribution.
                                                              (line   8)
* discontinuities, in ODE systems:       Evolution.           (line  77)
* Discrete Fourier Transforms, see FFT:  Fast Fourier Transforms.
                                                              (line   6)
* discrete Hankel transforms:            Discrete Hankel Transforms.
                                                              (line   6)
* Discrete Newton algorithm for multidimensional roots: Algorithms without Derivatives.
                                                              (line  26)
* Discrete random numbers:               General Discrete Distributions.
                                                              (line  52)
* Discrete random numbers, preprocessing: General Discrete Distributions.
                                                              (line  52)
* divided differences, polynomials:      Divided Difference Representation of Polynomials.
                                                              (line   6)
* division by zero, IEEE exceptions:     Setting up your IEEE environment.
                                                              (line   6)
* dollar sign $, shell prompt:           Conventions used in this manual.
                                                              (line  11)
* DOT, Level-1 BLAS:                     Level 1 GSL BLAS Interface.
                                                              (line   8)
* double factorial:                      Factorials.          (line  22)
* double precision, IEEE format:         Representation of floating point numbers.
                                                              (line  40)
* downloading GSL:                       Obtaining GSL.       (line   6)
* DWT initialization:                    DWT Initialization.  (line   6)
* DWT, mathematical definition:          DWT Definitions.     (line   6)
* DWT, one dimensional:                  DWT in one dimension.
                                                              (line   6)
* DWT, see wavelet transforms:           Wavelet Transforms.  (line   6)
* DWT, two dimensional:                  DWT in two dimension.
                                                              (line   6)
* e, defined as a macro:                 Mathematical Constants.
                                                              (line  10)
* E1(x), E2(x), Ei(x):                   Exponential Integral.
                                                              (line   6)
* eigenvalues and eigenvectors:          Eigensystems.        (line   6)
* elementary functions:                  Mathematical Functions.
                                                              (line   6)
* elementary operations:                 Elementary Operations.
                                                              (line   6)
* elliptic functions (Jacobi):           Elliptic Functions (Jacobi).
                                                              (line   6)
* elliptic integrals:                    Elliptic Integrals.  (line   6)
* energy function:                       Simulated Annealing. (line   6)
* energy, units of:                      Thermal Energy and Power.
                                                              (line   6)
* erf(x):                                Error Functions.     (line   6)
* erfc(x):                               Error Functions.     (line   6)
* Erlang distribution:                   The Gamma Distribution.
                                                              (line  16)
* error codes:                           Error Codes.         (line  13)
* error codes, reserved:                 Error Codes.         (line   6)
* error function:                        Error Functions.     (line   6)
* Error handlers:                        Error Handlers.      (line   6)
* error handling:                        Error Handling.      (line   6)
* error handling macros:                 Using GSL error reporting in your own functions.
                                                              (line   6)
* Errors:                                Error Handling.      (line   6)
* estimated standard deviation:          Statistics.          (line   6)
* estimated variance:                    Statistics.          (line   6)
* Eta Function:                          Eta Function.        (line   6)
* euclidean distance function, hypot:    Elementary Functions.
                                                              (line  23)
* Euler's constant, defined as a macro:  Mathematical Constants.
                                                              (line  58)
* evaluation of polynomials:             Polynomial Evaluation.
                                                              (line   6)
* evaluation of polynomials, in divided difference form: Divided Difference Representation of Polynomials.
                                                              (line   6)
* examples, conventions used in:         Conventions used in this manual.
                                                              (line   6)
* exceptions, C++:                       Compatibility with C++.
                                                              (line   6)
* exceptions, floating point:            Handling floating point exceptions.
                                                              (line   6)
* exceptions, IEEE arithmetic:           Setting up your IEEE environment.
                                                              (line   6)
* exchanging permutation elements:       Accessing permutation elements.
                                                              (line  18)
* exp:                                   Exponential Functions.
                                                              (line   6)
* expm1:                                 Elementary Functions.
                                                              (line  18)
* exponent, IEEE format:                 Representation of floating point numbers.
                                                              (line   6)
* Exponential distribution:              The Exponential Distribution.
                                                              (line   8)
* exponential function:                  Exponential Functions.
                                                              (line   6)
* exponential integrals:                 Exponential Integrals.
                                                              (line   6)
* Exponential power distribution:        The Exponential Power Distribution.
                                                              (line   8)
* exponential, difference from 1 computed accurately: Elementary Functions.
                                                              (line  18)
* exponentiation of complex number:      Elementary Complex Functions.
                                                              (line  16)
* extern inline:                         Inline functions.    (line   6)
* F-distribution:                        The F-distribution.  (line  16)
* factorial:                             Factorials.          (line   6)
* factorization of matrices:             Linear Algebra.      (line   6)
* false position algorithm for finding roots: Root Bracketing Algorithms.
                                                              (line  33)
* Fast Fourier Transforms, see FFT:      Fast Fourier Transforms.
                                                              (line   6)
* Fehlberg method, differential equations: Stepping Functions.
                                                              (line  96)
* Fermi-Dirac function:                  Fermi-Dirac Function.
                                                              (line   6)
* FFT:                                   Fast Fourier Transforms.
                                                              (line   6)
* FFT mathematical definition:           Mathematical Definitions.
                                                              (line   6)
* FFT of complex data, mixed-radix algorithm: Mixed-radix FFT routines for complex data.
                                                              (line   6)
* FFT of complex data, radix-2 algorithm: Radix-2 FFT routines for complex data.
                                                              (line   6)
* FFT of real data:                      Overview of real data FFTs.
                                                              (line   6)
* FFT of real data, mixed-radix algorithm: Mixed-radix FFT routines for real data.
                                                              (line   6)
* FFT of real data, radix-2 algorithm:   Radix-2 FFT routines for real data.
                                                              (line   6)
* FFT, complex data:                     Overview of complex data FFTs.
                                                              (line   6)
* finding minima:                        One dimensional Minimization.
                                                              (line   6)
* finding roots:                         One dimensional Root-Finding.
                                                              (line   6)
* finding zeros:                         One dimensional Root-Finding.
                                                              (line   6)
* fits, multi-parameter linear:          Multi-parameter fitting.
                                                              (line   6)
* fitting:                               Least-Squares Fitting.
                                                              (line   6)
* fitting, using Chebyshev polynomials:  Chebyshev Approximations.
                                                              (line   6)
* Fj(x), Fermi-Dirac integral:           Complete Fermi-Dirac Integrals.
                                                              (line   6)
* Fj(x,b), incomplete Fermi-Dirac integral: Incomplete Fermi-Dirac Integrals.
                                                              (line   6)
* flat distribution:                     The Flat (Uniform) Distribution.
                                                              (line   8)
* Fletcher-Reeves conjugate gradient algorithm, minimization: Multimin Algorithms with Derivatives.
                                                              (line  12)
* floating point exceptions:             Handling floating point exceptions.
                                                              (line   6)
* floating point numbers, approximate comparison: Approximate Comparison of Floating Point Numbers.
                                                              (line  13)
* floating point registers:              Examining floating point registers.
                                                              (line   6)
* force and energy, units of:            Force and Energy.    (line   6)
* Fortran range checking, equivalent in gcc: Accessing vector elements.
                                                              (line   6)
* Four-tap Generalized Feedback Shift Register: Random number generator algorithms.
                                                              (line 172)
* Fourier integrals, numerical:          QAWF adaptive integration for Fourier integrals.
                                                              (line   6)
* Fourier Transforms, see FFT:           Fast Fourier Transforms.
                                                              (line   6)
* Fractional Order Bessel Functions:     Regular Bessel Function - Fractional Order.
                                                              (line   6)
* free documentation:                    Free Software Needs Free Documentation.
                                                              (line   6)
* free software, explanation of:         GSL is Free Software.
                                                              (line   6)
* frexp:                                 Elementary Functions.
                                                              (line  49)
* functions, numerical differentiation:  Numerical Differentiation.
                                                              (line   6)
* fundamental constants:                 Fundamental Constants.
                                                              (line   6)
* Gamma distribution:                    The Gamma Distribution.
                                                              (line   9)
* gamma functions:                       Gamma Functions.     (line   6)
* Gauss-Kronrod quadrature:              Integrands without weight functions.
                                                              (line   6)
* Gaussian distribution:                 The Gaussian Distribution.
                                                              (line   7)
* Gaussian distribution, bivariate:      The Bivariate Gaussian Distribution.
                                                              (line   9)
* Gaussian Tail distribution:            The Gaussian Tail Distribution.
                                                              (line   8)
* gcc extensions, range-checking:        Accessing vector elements.
                                                              (line   6)
* gcc warning options:                   GCC warning options for numerical programs.
                                                              (line   6)
* gdb:                                   Using gdb.           (line   6)
* Gegenbauer functions:                  Gegenbauer Functions.
                                                              (line   6)
* GEMM, Level-3 BLAS:                    Level 3 GSL BLAS Interface.
                                                              (line  22)
* GEMV, Level-2 BLAS:                    Level 2 GSL BLAS Interface.
                                                              (line  20)
* general polynomial equations, solving: General Polynomial Equations.
                                                              (line   6)
* generalized eigensystems:              Real Generalized Nonsymmetric Eigensystems.
                                                              (line   6)
* generalized hermitian definite eigensystems: Complex Generalized Hermitian-Definite Eigensystems.
                                                              (line   6)
* generalized symmetric eigensystems:    Real Generalized Symmetric-Definite Eigensystems.
                                                              (line   6)
* Geometric random variates <1>:         The Hypergeometric Distribution.
                                                              (line   8)
* Geometric random variates:             The Geometric Distribution.
                                                              (line   8)
* GER, Level-2 BLAS:                     Level 2 GSL BLAS Interface.
                                                              (line 104)
* GERC, Level-2 BLAS:                    Level 2 GSL BLAS Interface.
                                                              (line 113)
* GERU, Level-2 BLAS:                    Level 2 GSL BLAS Interface.
                                                              (line 104)
* Givens Rotation, BLAS:                 Level 1 GSL BLAS Interface.
                                                              (line 116)
* Givens Rotation, Modified, BLAS:       Level 1 GSL BLAS Interface.
                                                              (line 135)
* GNU General Public License:            Introduction.        (line   6)
* golden section algorithm for finding minima: Minimization Algorithms.
                                                              (line  14)
* GSL_C99_INLINE:                        Inline functions.    (line   6)
* GSL_RNG_SEED:                          Random number generator initialization.
                                                              (line  17)
* gsl_sf_result:                         The gsl_sf_result struct.
                                                              (line   6)
* gsl_sf_result_e10:                     The gsl_sf_result struct.
                                                              (line   6)
* Gumbel distribution (Type 1):          The Type-1 Gumbel Distribution.
                                                              (line   8)
* Gumbel distribution (Type 2):          The Type-2 Gumbel Distribution.
                                                              (line   8)
* Haar wavelets:                         DWT Initialization.  (line  26)
* Hankel transforms, discrete:           Discrete Hankel Transforms.
                                                              (line   6)
* HAVE_INLINE:                           Inline functions.    (line   6)
* hazard function, normal distribution:  Probability functions.
                                                              (line  19)
* HBOOK:                                 Ntuple References and Further Reading.
                                                              (line   6)
* header files, including:               Compiling and Linking.
                                                              (line   6)
* heapsort:                              Sorting.             (line   6)
* HEMM, Level-3 BLAS:                    Level 3 GSL BLAS Interface.
                                                              (line  56)
* HEMV, Level-2 BLAS:                    Level 2 GSL BLAS Interface.
                                                              (line  85)
* HER, Level-2 BLAS:                     Level 2 GSL BLAS Interface.
                                                              (line 131)
* HER2, Level-2 BLAS:                    Level 2 GSL BLAS Interface.
                                                              (line 158)
* HER2K, Level-3 BLAS:                   Level 3 GSL BLAS Interface.
                                                              (line 181)
* HERK, Level-3 BLAS:                    Level 3 GSL BLAS Interface.
                                                              (line 140)
* hermitian matrix, complex, eigensystem: Complex Hermitian Matrices.
                                                              (line   9)
* Hessenberg decomposition:              Hessenberg Decomposition of Real Matrices.
                                                              (line   6)
* Hessenberg triangular decomposition:   Hessenberg-Triangular Decomposition of Real Matrices.
                                                              (line   6)
* histogram statistics:                  Histogram Statistics.
                                                              (line   6)
* histogram, from ntuple:                Histogramming ntuple values.
                                                              (line  35)
* histograms:                            Histograms.          (line   6)
* histograms, random sampling from:      The histogram probability distribution struct.
                                                              (line   6)
* Householder linear solver:             Householder solver for linear systems.
                                                              (line   6)
* Householder matrix:                    Householder Transformations.
                                                              (line   6)
* Householder transformation:            Householder Transformations.
                                                              (line   6)
* Hurwitz Zeta Function:                 Hurwitz Zeta Function.
                                                              (line   6)
* HYBRID algorithm, unscaled without derivatives: Algorithms without Derivatives.
                                                              (line  22)
* HYBRID algorithms for nonlinear systems: Algorithms using Derivatives.
                                                              (line  13)
* HYBRIDJ algorithm:                     Algorithms using Derivatives.
                                                              (line  67)
* HYBRIDS algorithm, scaled without derivatives: Algorithms without Derivatives.
                                                              (line  14)
* HYBRIDSJ algorithm:                    Algorithms using Derivatives.
                                                              (line  14)
* hydrogen atom:                         Coulomb Functions.   (line   6)
* hyperbolic cosine, inverse:            Elementary Functions.
                                                              (line  33)
* hyperbolic functions, complex numbers: Complex Hyperbolic Functions.
                                                              (line   6)
* hyperbolic integrals:                  Hyperbolic Integrals.
                                                              (line   6)
* hyperbolic sine, inverse:              Elementary Functions.
                                                              (line  37)
* hyperbolic space:                      Legendre Functions and Spherical Harmonics.
                                                              (line   6)
* hyperbolic tangent, inverse:           Elementary Functions.
                                                              (line  41)
* hypergeometric functions:              Hypergeometric Functions.
                                                              (line   6)
* hypergeometric random variates:        The Hypergeometric Distribution.
                                                              (line   6)
* hypot:                                 Elementary Functions.
                                                              (line  23)
* hypot function, special functions:     Circular Trigonometric Functions.
                                                              (line  17)
* i(x), Bessel Functions:                Regular Modified Spherical Bessel Functions.
                                                              (line   6)
* I(x), Bessel Functions:                Regular Modified Cylindrical Bessel Functions.
                                                              (line   6)
* identity matrix:                       Initializing matrix elements.
                                                              (line   6)
* identity permutation:                  Permutation allocation.
                                                              (line  20)
* IEEE exceptions:                       Setting up your IEEE environment.
                                                              (line   6)
* IEEE floating point:                   IEEE floating-point arithmetic.
                                                              (line   6)
* IEEE format for floating point numbers: Representation of floating point numbers.
                                                              (line   6)
* IEEE infinity, defined as a macro:     Infinities and Not-a-number.
                                                              (line   6)
* IEEE NaN, defined as a macro:          Infinities and Not-a-number.
                                                              (line   6)
* illumination, units of:                Light and Illumination.
                                                              (line   6)
* imperial units:                        Imperial Units.      (line   6)
* Implicit Euler method:                 Stepping Functions.  (line 106)
* Implicit Runge-Kutta method:           Stepping Functions.  (line 112)
* importance sampling, VEGAS:            VEGAS.               (line   6)
* including GSL header files:            Compiling and Linking.
                                                              (line   6)
* incomplete Beta function, normalized:  Incomplete Beta Function.
                                                              (line   9)
* incomplete Fermi-Dirac integral:       Incomplete Fermi-Dirac Integrals.
                                                              (line   6)
* incomplete Gamma function:             Incomplete Gamma Functions.
                                                              (line  16)
* indirect sorting:                      Sorting objects.     (line  57)
* indirect sorting, of vector elements:  Sorting vectors.     (line  31)
* infinity, defined as a macro:          Infinities and Not-a-number.
                                                              (line   6)
* infinity, IEEE format:                 Representation of floating point numbers.
                                                              (line  27)
* info-gsl mailing list:                 Obtaining GSL.       (line   6)
* initial value problems, differential equations: Ordinary Differential Equations.
                                                              (line   6)
* initializing matrices:                 Initializing matrix elements.
                                                              (line   6)
* initializing vectors:                  Initializing vector elements.
                                                              (line   6)
* inline functions:                      Inline functions.    (line   6)
* integer powers:                        Power Function.      (line   6)
* integrals, exponential:                Exponential Integrals.
                                                              (line   6)
* integration, numerical (quadrature):   Numerical Integration.
                                                              (line   6)
* interpolation:                         Interpolation.       (line   6)
* interpolation, using Chebyshev polynomials: Chebyshev Approximations.
                                                              (line   6)
* inverse complex trigonometric functions: Inverse Complex Trigonometric Functions.
                                                              (line   6)
* inverse cumulative distribution functions: Random Number Distributions.
                                                              (line   6)
* inverse hyperbolic cosine:             Elementary Functions.
                                                              (line  33)
* inverse hyperbolic functions, complex numbers: Inverse Complex Hyperbolic Functions.
                                                              (line   6)
* inverse hyperbolic sine:               Elementary Functions.
                                                              (line  37)
* inverse hyperbolic tangent:            Elementary Functions.
                                                              (line  41)
* inverse of a matrix, by LU decomposition: LU Decomposition. (line  69)
* inverting a permutation:               Permutation functions.
                                                              (line  11)
* Irregular Cylindrical Bessel Functions: Irregular Cylindrical Bessel Functions.
                                                              (line   6)
* Irregular Modified Bessel Functions, Fractional Order: Irregular Modified Bessel Functions - Fractional Order.
                                                              (line   6)
* Irregular Modified Cylindrical Bessel Functions: Irregular Modified Cylindrical Bessel Functions.
                                                              (line   6)
* Irregular Modified Spherical Bessel Functions: Irregular Modified Spherical Bessel Functions.
                                                              (line   6)
* Irregular Spherical Bessel Functions:  Irregular Spherical Bessel Functions.
                                                              (line   6)
* iterating through combinations:        Combination functions.
                                                              (line   7)
* iterating through multisets:           Multiset functions.  (line   7)
* iterating through permutations:        Permutation functions.
                                                              (line  15)
* iterative refinement of solutions in linear systems: LU Decomposition.
                                                              (line  57)
* j(x), Bessel Functions:                Regular Spherical Bessel Functions.
                                                              (line   6)
* J(x), Bessel Functions:                Regular Cylindrical Bessel Functions.
                                                              (line   6)
* Jacobi elliptic functions:             Elliptic Functions (Jacobi).
                                                              (line   6)
* Jacobi orthogonalization:              Singular Value Decomposition.
                                                              (line  58)
* Jacobian matrix, fitting:              Overview of Nonlinear Least-Squares Fitting.
                                                              (line  34)
* Jacobian matrix, ODEs:                 Defining the ODE System.
                                                              (line  34)
* Jacobian matrix, root finding:         Overview of Multidimensional Root Finding.
                                                              (line  42)
* k(x), Bessel Functions:                Irregular Modified Spherical Bessel Functions.
                                                              (line   6)
* K(x), Bessel Functions:                Irregular Modified Cylindrical Bessel Functions.
                                                              (line   6)
* knots, basis splines:                  Constructing the knots vector.
                                                              (line   6)
* kurtosis:                              Higher moments (skewness and kurtosis).
                                                              (line   6)
* Laguerre functions:                    Laguerre Functions.  (line   6)
* Lambert function:                      Lambert W Functions. (line   6)
* Landau distribution:                   The Landau Distribution.
                                                              (line   8)
* LAPACK:                                Eigenvalue and Eigenvector References.
                                                              (line  18)
* Laplace distribution:                  The Laplace Distribution.
                                                              (line   7)
* LD_LIBRARY_PATH:                       Shared Libraries.    (line   6)
* ldexp:                                 Elementary Functions.
                                                              (line  45)
* leading dimension, matrices:           Matrices.            (line   6)
* least squares fit:                     Least-Squares Fitting.
                                                              (line   6)
* least squares fitting, nonlinear:      Nonlinear Least-Squares Fitting.
                                                              (line   7)
* least squares, covariance of best-fit parameters: Computing the covariance matrix of best fit parameters.
                                                              (line   6)
* Legendre forms of elliptic integrals:  Definition of Legendre Forms.
                                                              (line   6)
* Legendre functions:                    Legendre Functions and Spherical Harmonics.
                                                              (line   6)
* Legendre polynomials:                  Legendre Functions and Spherical Harmonics.
                                                              (line   6)
* length, computed accurately using hypot: Elementary Functions.
                                                              (line  23)
* Levenberg-Marquardt algorithms:        Minimization Algorithms using Derivatives.
                                                              (line  12)
* Levin u-transform:                     Series Acceleration. (line   6)
* Levy distribution:                     The Levy alpha-Stable Distributions.
                                                              (line   9)
* Levy distribution, skew:               The Levy skew alpha-Stable Distribution.
                                                              (line   9)
* libraries, linking with:               Linking programs with the library.
                                                              (line   6)
* libraries, shared:                     Shared Libraries.    (line   6)
* license of GSL:                        Introduction.        (line   6)
* light, units of:                       Light and Illumination.
                                                              (line   6)
* linear algebra:                        Linear Algebra.      (line   6)
* linear algebra, BLAS:                  BLAS Support.        (line   6)
* linear interpolation:                  Interpolation Types. (line   9)
* linear regression:                     Linear regression.   (line   6)
* linear systems, refinement of solutions: LU Decomposition.  (line  57)
* linear systems, solution of:           LU Decomposition.    (line  39)
* linking with GSL libraries:            Linking programs with the library.
                                                              (line   6)
* LMDER algorithm:                       Minimization Algorithms using Derivatives.
                                                              (line  13)
* log1p:                                 Elementary Functions.
                                                              (line  13)
* logarithm and related functions:       Logarithm and Related Functions.
                                                              (line   6)
* logarithm of Beta function:            Beta Functions.      (line  16)
* logarithm of combinatorial factor C(m,n): Factorials.       (line  48)
* logarithm of complex number:           Elementary Complex Functions.
                                                              (line  29)
* logarithm of cosh function, special functions: Hyperbolic Trigonometric Functions.
                                                              (line  12)
* logarithm of double factorial:         Factorials.          (line  36)
* logarithm of factorial:                Factorials.          (line  29)
* logarithm of Gamma function:           Gamma Functions.     (line  24)
* logarithm of Pochhammer symbol:        Pochhammer Symbol.   (line  18)
* logarithm of sinh function, special functions: Hyperbolic Trigonometric Functions.
                                                              (line   8)
* logarithm of the determinant of a matrix: LU Decomposition. (line  91)
* logarithm, computed accurately near 1: Elementary Functions.
                                                              (line  13)
* Logarithmic random variates:           The Logarithmic Distribution.
                                                              (line   8)
* Logistic distribution:                 The Logistic Distribution.
                                                              (line   7)
* Lognormal distribution:                The Lognormal Distribution.
                                                              (line   8)
* long double:                           Long double.         (line   6)
* low discrepancy sequences:             Quasi-Random Sequences.
                                                              (line   6)
* Low-level CBLAS:                       GSL CBLAS Library.   (line   6)
* LU decomposition:                      LU Decomposition.    (line   6)
* macros for mathematical constants:     Mathematical Constants.
                                                              (line   6)
* magnitude of complex number:           Properties of complex numbers.
                                                              (line  11)
* mailing list archives:                 Further Information. (line   6)
* mailing list for GSL announcements:    Obtaining GSL.       (line   6)
* mailing list, bug-gsl:                 Reporting Bugs.      (line   6)
* mantissa, IEEE format:                 Representation of floating point numbers.
                                                              (line   6)
* mass, units of:                        Mass and Weight.     (line   6)
* mathematical constants, defined as macros: Mathematical Constants.
                                                              (line   6)
* mathematical functions, elementary:    Mathematical Functions.
                                                              (line   6)
* Mathieu Function Characteristic Values: Mathieu Function Characteristic Values.
                                                              (line   6)
* Mathieu functions:                     Mathieu Functions.   (line   6)
* matrices <1>:                          Matrices.            (line   6)
* matrices:                              Vectors and Matrices.
                                                              (line   6)
* matrices, initializing:                Initializing matrix elements.
                                                              (line   6)
* matrices, range-checking:              Accessing matrix elements.
                                                              (line   6)
* matrix determinant:                    LU Decomposition.    (line  83)
* matrix diagonal:                       Creating row and column views.
                                                              (line  62)
* matrix factorization:                  Linear Algebra.      (line   6)
* matrix inverse:                        LU Decomposition.    (line  69)
* matrix square root, Cholesky decomposition: Cholesky Decomposition.
                                                              (line   6)
* matrix subdiagonal:                    Creating row and column views.
                                                              (line  74)
* matrix superdiagonal:                  Creating row and column views.
                                                              (line  86)
* matrix, constant:                      Initializing matrix elements.
                                                              (line   6)
* matrix, identity:                      Initializing matrix elements.
                                                              (line   6)
* matrix, operations:                    BLAS Support.        (line   6)
* matrix, zero:                          Initializing matrix elements.
                                                              (line   6)
* max:                                   Statistics.          (line   6)
* maximal phase, Daubechies wavelets:    DWT Initialization.  (line  20)
* maximization, see minimization:        One dimensional Minimization.
                                                              (line   6)
* maximum of two numbers:                Maximum and Minimum functions.
                                                              (line  11)
* maximum value, from histogram:         Histogram Statistics.
                                                              (line   6)
* mean:                                  Statistics.          (line   6)
* mean value, from histogram:            Histogram Statistics.
                                                              (line  24)
* Mills' ratio, inverse:                 Probability functions.
                                                              (line  19)
* min:                                   Statistics.          (line   6)
* minimization, BFGS algorithm:          Multimin Algorithms with Derivatives.
                                                              (line  37)
* minimization, caveats:                 Minimization Caveats.
                                                              (line   6)
* minimization, conjugate gradient algorithm: Multimin Algorithms with Derivatives.
                                                              (line  12)
* minimization, multidimensional:        Multidimensional Minimization.
                                                              (line   6)
* minimization, one-dimensional:         One dimensional Minimization.
                                                              (line   6)
* minimization, overview:                Minimization Overview.
                                                              (line   6)
* minimization, Polak-Ribiere algorithm: Multimin Algorithms with Derivatives.
                                                              (line  29)
* minimization, providing a function to minimize: Providing the function to minimize.
                                                              (line   6)
* minimization, simplex algorithm:       Multimin Algorithms without Derivatives.
                                                              (line  11)
* minimization, steepest descent algorithm: Multimin Algorithms with Derivatives.
                                                              (line  57)
* minimization, stopping parameters:     Minimization Stopping Parameters.
                                                              (line   6)
* minimum finding, Brent's method:       Minimization Algorithms.
                                                              (line  32)
* minimum finding, golden section algorithm: Minimization Algorithms.
                                                              (line  14)
* minimum of two numbers:                Maximum and Minimum functions.
                                                              (line  15)
* minimum value, from histogram:         Histogram Statistics.
                                                              (line   6)
* MINPACK, minimization algorithms <1>:  Minimization Algorithms using Derivatives.
                                                              (line  13)
* MINPACK, minimization algorithms:      Algorithms using Derivatives.
                                                              (line  14)
* MISCFUN:                               Special Functions References and Further Reading.
                                                              (line  11)
* MISER monte carlo integration:         MISER.               (line   6)
* Mixed-radix FFT, complex data:         Mixed-radix FFT routines for complex data.
                                                              (line   6)
* Mixed-radix FFT, real data:            Mixed-radix FFT routines for real data.
                                                              (line   6)
* Modified Bessel Functions, Fractional Order: Regular Modified Bessel Functions - Fractional Order.
                                                              (line   6)
* Modified Clenshaw-Curtis quadrature:   Integrands with weight functions.
                                                              (line   6)
* Modified Cylindrical Bessel Functions: Regular Modified Cylindrical Bessel Functions.
                                                              (line   6)
* Modified Givens Rotation, BLAS:        Level 1 GSL BLAS Interface.
                                                              (line 135)
* Modified Newton's method for nonlinear systems: Algorithms using Derivatives.
                                                              (line  92)
* Modified Spherical Bessel Functions:   Regular Modified Spherical Bessel Functions.
                                                              (line   6)
* Monte Carlo integration:               Monte Carlo Integration.
                                                              (line   6)
* MRG, multiple recursive random number generator: Random number generator algorithms.
                                                              (line 119)
* MT19937 random number generator:       Random number generator algorithms.
                                                              (line  20)
* multi-parameter regression:            Multi-parameter fitting.
                                                              (line   6)
* multidimensional integration:          Monte Carlo Integration.
                                                              (line   6)
* multidimensional root finding, Broyden algorithm: Algorithms without Derivatives.
                                                              (line  45)
* multidimensional root finding, overview: Overview of Multidimensional Root Finding.
                                                              (line   6)
* multidimensional root finding, providing a function to solve: Providing the multidimensional system of equations to solve.
                                                              (line   6)
* Multimin, caveats:                     Multimin Caveats.    (line   6)
* Multinomial distribution:              The Multinomial Distribution.
                                                              (line   8)
* multiplication:                        Elementary Operations.
                                                              (line   6)
* multisets:                             Multisets.           (line   6)
* multistep methods, ODEs:               Stepping Functions.  (line 129)
* N-dimensional random direction vector: Spherical Vector Distributions.
                                                              (line  42)
* NaN, defined as a macro:               Infinities and Not-a-number.
                                                              (line   6)
* nautical units:                        Speed and Nautical Units.
                                                              (line   6)
* Negative Binomial distribution, random variates: The Negative Binomial Distribution.
                                                              (line   8)
* Nelder-Mead simplex algorithm for minimization: Multimin Algorithms without Derivatives.
                                                              (line  11)
* Newton algorithm, discrete:            Algorithms without Derivatives.
                                                              (line  26)
* Newton algorithm, globally convergent: Algorithms using Derivatives.
                                                              (line  92)
* Newton's method for finding roots:     Root Finding Algorithms using Derivatives.
                                                              (line  16)
* Newton's method for systems of nonlinear equations: Algorithms using Derivatives.
                                                              (line  73)
* Niederreiter sequence:                 Quasi-Random Sequences.
                                                              (line   6)
* NIST Statistical Reference Datasets:   Fitting References and Further Reading.
                                                              (line  16)
* non-normalized incomplete Gamma function: Incomplete Gamma Functions.
                                                              (line   9)
* nonlinear equation, solutions of:      One dimensional Root-Finding.
                                                              (line   6)
* nonlinear fitting, stopping parameters: Search Stopping Parameters for Minimization Algorithms.
                                                              (line   6)
* nonlinear functions, minimization:     One dimensional Minimization.
                                                              (line   6)
* nonlinear least squares fitting:       Nonlinear Least-Squares Fitting.
                                                              (line   7)
* nonlinear least squares fitting, overview: Overview of Nonlinear Least-Squares Fitting.
                                                              (line   6)
* nonlinear systems of equations, solution of: Multidimensional Root-Finding.
                                                              (line   6)
* nonsymmetric matrix, real, eigensystem: Real Nonsymmetric Matrices.
                                                              (line   6)
* Nordsieck form:                        Stepping Functions.  (line 129)
* normalized form, IEEE format:          Representation of floating point numbers.
                                                              (line  14)
* normalized incomplete Beta function:   Incomplete Beta Function.
                                                              (line   9)
* Not-a-number, defined as a macro:      Infinities and Not-a-number.
                                                              (line   6)
* NRM2, Level-1 BLAS:                    Level 1 GSL BLAS Interface.
                                                              (line  36)
* ntuples:                               N-tuples.            (line   6)
* nuclear physics, constants:            Atomic and Nuclear Physics.
                                                              (line   6)
* numerical constants, defined as macros: Mathematical Constants.
                                                              (line   6)
* numerical derivatives:                 Numerical Differentiation.
                                                              (line   6)
* numerical integration (quadrature):    Numerical Integration.
                                                              (line   6)
* obtaining GSL:                         Obtaining GSL.       (line   6)
* ODEs, initial value problems:          Ordinary Differential Equations.
                                                              (line   6)
* optimization, combinatorial:           Simulated Annealing. (line   6)
* optimization, see minimization:        One dimensional Minimization.
                                                              (line   6)
* optimized functions, alternatives:     Alternative optimized functions.
                                                              (line   6)
* ordering, matrix elements:             Matrices.            (line   6)
* ordinary differential equations, initial value problem: Ordinary Differential Equations.
                                                              (line   6)
* oscillatory functions, numerical integration of: QAWO adaptive integration for oscillatory functions.
                                                              (line   6)
* overflow, IEEE exceptions:             Setting up your IEEE environment.
                                                              (line   6)
* Pareto distribution:                   The Pareto Distribution.
                                                              (line   8)
* PAW:                                   Ntuple References and Further Reading.
                                                              (line   6)
* permutations:                          Permutations.        (line   6)
* physical constants:                    Physical Constants.  (line   6)
* physical dimension, matrices:          Matrices.            (line   6)
* pi, defined as a macro:                Mathematical Constants.
                                                              (line  28)
* plain Monte Carlo:                     PLAIN Monte Carlo.   (line   6)
* Pochhammer symbol:                     Pochhammer Symbol.   (line   9)
* Poisson random numbers:                The Poisson Distribution.
                                                              (line   8)
* Polak-Ribiere algorithm, minimization: Multimin Algorithms with Derivatives.
                                                              (line  29)
* polar form of complex numbers:         Representation of complex numbers.
                                                              (line   6)
* polar to rectangular conversion:       Conversion Functions.
                                                              (line   6)
* polygamma functions:                   Psi (Digamma) Function.
                                                              (line   6)
* polynomial evaluation:                 Polynomial Evaluation.
                                                              (line   6)
* polynomial interpolation:              Interpolation Types. (line  13)
* polynomials, roots of:                 Polynomials.         (line   6)
* power function:                        Power Function.      (line   6)
* power of complex number:               Elementary Complex Functions.
                                                              (line  16)
* power, units of:                       Thermal Energy and Power.
                                                              (line   6)
* precision, IEEE arithmetic:            Setting up your IEEE environment.
                                                              (line   6)
* predictor-corrector method, ODEs:      Stepping Functions.  (line 129)
* prefixes:                              Prefixes.            (line   6)
* pressure, units of:                    Pressure.            (line   6)
* Prince-Dormand, Runge-Kutta method:    Stepping Functions.  (line 103)
* printers units:                        Printers Units.      (line   6)
* probability distribution, from histogram: The histogram probability distribution struct.
                                                              (line   6)
* probability distributions, from histograms: Resampling from histograms.
                                                              (line   6)
* projection of ntuples:                 Histogramming ntuple values.
                                                              (line  35)
* psi function:                          Psi (Digamma) Function.
                                                              (line   6)
* QAG quadrature algorithm:              QAG adaptive integration.
                                                              (line   6)
* QAGI quadrature algorithm:             QAGI adaptive integration on infinite intervals.
                                                              (line   6)
* QAGP quadrature algorithm:             QAGP adaptive integration with known singular points.
                                                              (line   6)
* QAGS quadrature algorithm:             QAGS adaptive integration with singularities.
                                                              (line   6)
* QAWC quadrature algorithm:             QAWC adaptive integration for Cauchy principal values.
                                                              (line   6)
* QAWF quadrature algorithm:             QAWF adaptive integration for Fourier integrals.
                                                              (line   6)
* QAWO quadrature algorithm:             QAWO adaptive integration for oscillatory functions.
                                                              (line   6)
* QAWS quadrature algorithm:             QAWS adaptive integration for singular functions.
                                                              (line   6)
* QNG quadrature algorithm:              QNG non-adaptive Gauss-Kronrod integration.
                                                              (line   6)
* QR decomposition:                      QR Decomposition.    (line   6)
* QR decomposition with column pivoting: QR Decomposition with Column Pivoting.
                                                              (line   6)
* QUADPACK:                              Numerical Integration.
                                                              (line   6)
* quadratic equation, solving:           Quadratic Equations. (line   6)
* quadrature:                            Numerical Integration.
                                                              (line   6)
* quantile functions:                    Random Number Distributions.
                                                              (line   6)
* quasi-random sequences:                Quasi-Random Sequences.
                                                              (line   6)
* R250 shift-register random number generator: Other random number generators.
                                                              (line  60)
* Racah coefficients:                    Coupling Coefficients.
                                                              (line   6)
* Radial Mathieu Functions:              Radial Mathieu Functions.
                                                              (line   6)
* radioactivity, units of:               Radioactivity.       (line   6)
* Radix-2 FFT for real data:             Radix-2 FFT routines for real data.
                                                              (line   6)
* Radix-2 FFT, complex data:             Radix-2 FFT routines for complex data.
                                                              (line   6)
* rand, BSD random number generator:     Unix random number generators.
                                                              (line  17)
* rand48 random number generator:        Unix random number generators.
                                                              (line  58)
* random number distributions:           Random Number Distributions.
                                                              (line   6)
* random number generators:              Random Number Generation.
                                                              (line   6)
* random sampling from histograms:       The histogram probability distribution struct.
                                                              (line   6)
* RANDU random number generator:         Other random number generators.
                                                              (line 105)
* RANF random number generator:          Other random number generators.
                                                              (line  23)
* range:                                 Statistics.          (line   6)
* range-checking for matrices:           Accessing matrix elements.
                                                              (line   6)
* range-checking for vectors:            Accessing vector elements.
                                                              (line   6)
* RANLUX random number generator:        Random number generator algorithms.
                                                              (line  71)
* RANLXD random number generator:        Random number generator algorithms.
                                                              (line  65)
* RANLXS random number generator:        Random number generator algorithms.
                                                              (line  47)
* RANMAR random number generator:        Other random number generators.
                                                              (line  54)
* Rayleigh distribution:                 The Rayleigh Distribution.
                                                              (line   7)
* Rayleigh Tail distribution:            The Rayleigh Tail Distribution.
                                                              (line   8)
* real nonsymmetric matrix, eigensystem: Real Nonsymmetric Matrices.
                                                              (line   6)
* real symmetric matrix, eigensystem:    Real Symmetric Matrices.
                                                              (line   6)
* Reciprocal Gamma function:             Gamma Functions.     (line  51)
* rectangular to polar conversion:       Conversion Functions.
                                                              (line   6)
* recursive stratified sampling, MISER:  MISER.               (line   6)
* reduction of angular variables:        Restriction Functions.
                                                              (line   6)
* refinement of solutions in linear systems: LU Decomposition.
                                                              (line  57)
* regression, least squares:             Least-Squares Fitting.
                                                              (line   6)
* Regular Bessel Functions, Fractional Order: Regular Bessel Function - Fractional Order.
                                                              (line   6)
* Regular Bessel Functions, Zeros of:    Zeros of Regular Bessel Functions.
                                                              (line   6)
* Regular Cylindrical Bessel Functions:  Regular Cylindrical Bessel Functions.
                                                              (line   6)
* Regular Modified Bessel Functions, Fractional Order: Regular Modified Bessel Functions - Fractional Order.
                                                              (line   6)
* Regular Modified Cylindrical Bessel Functions: Regular Modified Cylindrical Bessel Functions.
                                                              (line   6)
* Regular Modified Spherical Bessel Functions: Regular Modified Spherical Bessel Functions.
                                                              (line   6)
* Regular Spherical Bessel Functions:    Regular Spherical Bessel Functions.
                                                              (line   6)
* Regulated Gamma function:              Gamma Functions.     (line  42)
* relative Pochhammer symbol:            Pochhammer Symbol.   (line  31)
* reporting bugs in GSL:                 Reporting Bugs.      (line   6)
* representations of complex numbers:    Representation of complex numbers.
                                                              (line   6)
* resampling from histograms:            Resampling from histograms.
                                                              (line   6)
* residual, in nonlinear systems of equations <1>: Search Stopping Parameters for Minimization Algorithms.
                                                              (line  30)
* residual, in nonlinear systems of equations: Search Stopping Parameters for the multidimensional solver.
                                                              (line  31)
* reversing a permutation:               Permutation functions.
                                                              (line   7)
* Riemann Zeta Function:                 Riemann Zeta Function.
                                                              (line   6)
* RK2, Runge-Kutta method:               Stepping Functions.  (line  88)
* RK4, Runge-Kutta method:               Stepping Functions.  (line  91)
* RKF45, Runge-Kutta-Fehlberg method:    Stepping Functions.  (line  96)
* root finding:                          One dimensional Root-Finding.
                                                              (line   6)
* root finding, bisection algorithm:     Root Bracketing Algorithms.
                                                              (line  17)
* root finding, Brent's method:          Root Bracketing Algorithms.
                                                              (line  50)
* root finding, caveats:                 Root Finding Caveats.
                                                              (line   6)
* root finding, false position algorithm: Root Bracketing Algorithms.
                                                              (line  33)
* root finding, initial guess:           Search Bounds and Guesses.
                                                              (line   6)
* root finding, Newton's method:         Root Finding Algorithms using Derivatives.
                                                              (line  16)
* root finding, overview:                Root Finding Overview.
                                                              (line   6)
* root finding, providing a function to solve: Providing the function to solve.
                                                              (line   6)
* root finding, search bounds:           Search Bounds and Guesses.
                                                              (line   6)
* root finding, secant method:           Root Finding Algorithms using Derivatives.
                                                              (line  30)
* root finding, Steffenson's method:     Root Finding Algorithms using Derivatives.
                                                              (line  61)
* root finding, stopping parameters <1>: Search Stopping Parameters for the multidimensional solver.
                                                              (line   6)
* root finding, stopping parameters:     Search Stopping Parameters.
                                                              (line   6)
* roots:                                 One dimensional Root-Finding.
                                                              (line   6)
* ROTG, Level-1 BLAS:                    Level 1 GSL BLAS Interface.
                                                              (line 116)
* rounding mode:                         Setting up your IEEE environment.
                                                              (line   6)
* Runge-Kutta Cash-Karp method:          Stepping Functions.  (line 100)
* Runge-Kutta methods, ordinary differential equations: Stepping Functions.
                                                              (line  88)
* Runge-Kutta Prince-Dormand method:     Stepping Functions.  (line 103)
* safe comparison of floating point numbers: Approximate Comparison of Floating Point Numbers.
                                                              (line  13)
* safeguarded step-length algorithm:     Minimization Algorithms.
                                                              (line  48)
* sampling from histograms <1>:          The histogram probability distribution struct.
                                                              (line   6)
* sampling from histograms:              Resampling from histograms.
                                                              (line   6)
* SAXPY, Level-1 BLAS:                   Level 1 GSL BLAS Interface.
                                                              (line  96)
* SCAL, Level-1 BLAS:                    Level 1 GSL BLAS Interface.
                                                              (line 109)
* schedule, cooling:                     Simulated Annealing algorithm.
                                                              (line  23)
* se(q,x), Mathieu function:             Angular Mathieu Functions.
                                                              (line   6)
* secant method for finding roots:       Root Finding Algorithms using Derivatives.
                                                              (line  30)
* selection function, ntuples:           Histogramming ntuple values.
                                                              (line  13)
* series, acceleration:                  Series Acceleration. (line   6)
* shared libraries:                      Shared Libraries.    (line   6)
* shell prompt:                          Conventions used in this manual.
                                                              (line   6)
* Shi(x):                                Hyperbolic Integrals.
                                                              (line   6)
* shift-register random number generator: Other random number generators.
                                                              (line  60)
* Si(x):                                 Trigonometric Integrals.
                                                              (line   6)
* sign bit, IEEE format:                 Representation of floating point numbers.
                                                              (line   6)
* sign of the determinant of a matrix:   LU Decomposition.    (line  99)
* simplex algorithm, minimization:       Multimin Algorithms without Derivatives.
                                                              (line  11)
* simulated annealing:                   Simulated Annealing. (line   6)
* sin, of complex number:                Complex Trigonometric Functions.
                                                              (line   7)
* sine function, special functions:      Circular Trigonometric Functions.
                                                              (line   8)
* single precision, IEEE format:         Representation of floating point numbers.
                                                              (line  31)
* singular functions, numerical integration of: QAWS adaptive integration for singular functions.
                                                              (line   6)
* singular points, specifying positions in quadrature: QAGP adaptive integration with known singular points.
                                                              (line   6)
* singular value decomposition:          Singular Value Decomposition.
                                                              (line   6)
* Skew Levy distribution:                The Levy skew alpha-Stable Distribution.
                                                              (line   9)
* skewness:                              Higher moments (skewness and kurtosis).
                                                              (line   6)
* slope, see numerical derivative:       Numerical Differentiation.
                                                              (line   6)
* Sobol sequence:                        Quasi-Random Sequences.
                                                              (line   6)
* solution of linear system by Householder transformations: Householder solver for linear systems.
                                                              (line   6)
* solution of linear systems, Ax=b:      Linear Algebra.      (line   6)
* solving a nonlinear equation:          One dimensional Root-Finding.
                                                              (line   6)
* solving nonlinear systems of equations: Multidimensional Root-Finding.
                                                              (line   6)
* sorting:                               Sorting.             (line   6)
* sorting eigenvalues and eigenvectors:  Sorting Eigenvalues and Eigenvectors.
                                                              (line   6)
* sorting vector elements:               Sorting vectors.     (line  23)
* source code, reuse in applications:    Code Reuse.          (line   6)
* special functions:                     Special Functions.   (line   6)
* Spherical Bessel Functions:            Regular Spherical Bessel Functions.
                                                              (line   6)
* spherical harmonics:                   Legendre Functions and Spherical Harmonics.
                                                              (line   6)
* spherical random variates, 2D:         Spherical Vector Distributions.
                                                              (line  14)
* spherical random variates, 3D:         Spherical Vector Distributions.
                                                              (line  33)
* spherical random variates, N-dimensional: Spherical Vector Distributions.
                                                              (line  42)
* spline:                                Interpolation.       (line   6)
* splines, basis:                        Basis Splines.       (line   6)
* square root of a matrix, Cholesky decomposition: Cholesky Decomposition.
                                                              (line   6)
* square root of complex number:         Elementary Complex Functions.
                                                              (line   7)
* standard deviation:                    Statistics.          (line   6)
* standard deviation, from histogram:    Histogram Statistics.
                                                              (line  30)
* standards conformance, ANSI C:         Using the library.   (line   6)
* Statistical Reference Datasets (StRD): Fitting References and Further Reading.
                                                              (line  16)
* statistics:                            Statistics.          (line   6)
* statistics, from histogram:            Histogram Statistics.
                                                              (line   6)
* steepest descent algorithm, minimization: Multimin Algorithms with Derivatives.
                                                              (line  57)
* Steffenson's method for finding roots: Root Finding Algorithms using Derivatives.
                                                              (line  61)
* stratified sampling in Monte Carlo integration: Monte Carlo Integration.
                                                              (line   6)
* stride, of vector index:               Vectors.             (line   6)
* Student t-distribution:                The t-distribution.  (line  15)
* subdiagonal, of a matrix:              Creating row and column views.
                                                              (line  74)
* summation, acceleration:               Series Acceleration. (line   6)
* superdiagonal, matrix:                 Creating row and column views.
                                                              (line  86)
* SVD:                                   Singular Value Decomposition.
                                                              (line   6)
* SWAP, Level-1 BLAS:                    Level 1 GSL BLAS Interface.
                                                              (line  76)
* swapping permutation elements:         Accessing permutation elements.
                                                              (line  18)
* SYMM, Level-3 BLAS:                    Level 3 GSL BLAS Interface.
                                                              (line  41)
* symmetric matrix, real, eigensystem:   Real Symmetric Matrices.
                                                              (line   6)
* SYMV, Level-2 BLAS:                    Level 2 GSL BLAS Interface.
                                                              (line  71)
* synchrotron functions:                 Synchrotron Functions.
                                                              (line   6)
* SYR, Level-2 BLAS:                     Level 2 GSL BLAS Interface.
                                                              (line 120)
* SYR2, Level-2 BLAS:                    Level 2 GSL BLAS Interface.
                                                              (line 144)
* SYR2K, Level-3 BLAS:                   Level 3 GSL BLAS Interface.
                                                              (line 164)
* SYRK, Level-3 BLAS:                    Level 3 GSL BLAS Interface.
                                                              (line 126)
* systems of equations, nonlinear:       Multidimensional Root-Finding.
                                                              (line   6)
* t-distribution:                        The t-distribution.  (line  15)
* t-test:                                Statistics.          (line   6)
* tangent of complex number:             Complex Trigonometric Functions.
                                                              (line  15)
* Tausworthe random number generator:    Random number generator algorithms.
                                                              (line 137)
* Taylor coefficients, computation of:   Factorials.          (line  54)
* testing combination for validity:      Combination properties.
                                                              (line  18)
* testing multiset for validity:         Multiset properties. (line  17)
* testing permutation for validity:      Permutation properties.
                                                              (line  14)
* thermal energy, units of:              Thermal Energy and Power.
                                                              (line   6)
* time units:                            Measurement of Time. (line   6)
* trailing dimension, matrices:          Matrices.            (line   6)
* transformation, Householder:           Householder Transformations.
                                                              (line   6)
* transforms, Hankel:                    Discrete Hankel Transforms.
                                                              (line   6)
* transforms, wavelet:                   Wavelet Transforms.  (line   6)
* transport functions:                   Transport Functions. (line   6)
* traveling salesman problem:            Traveling Salesman Problem.
                                                              (line   6)
* tridiagonal decomposition <1>:         Tridiagonal Decomposition of Hermitian Matrices.
                                                              (line   6)
* tridiagonal decomposition:             Tridiagonal Decomposition of Real Symmetric Matrices.
                                                              (line   6)
* tridiagonal systems:                   Tridiagonal Systems. (line   6)
* trigonometric functions:               Trigonometric Functions.
                                                              (line   6)
* trigonometric functions of complex numbers: Complex Trigonometric Functions.
                                                              (line   6)
* trigonometric integrals:               Trigonometric Integrals.
                                                              (line   6)
* TRMM, Level-3 BLAS:                    Level 3 GSL BLAS Interface.
                                                              (line  78)
* TRMV, Level-2 BLAS:                    Level 2 GSL BLAS Interface.
                                                              (line  36)
* TRSM, Level-3 BLAS:                    Level 3 GSL BLAS Interface.
                                                              (line 102)
* TRSV, Level-2 BLAS:                    Level 2 GSL BLAS Interface.
                                                              (line  57)
* TSP:                                   Traveling Salesman Problem.
                                                              (line   6)
* TT800 random number generator:         Other random number generators.
                                                              (line  75)
* two dimensional Gaussian distribution: The Bivariate Gaussian Distribution.
                                                              (line   9)
* two dimensional histograms:            Two dimensional histograms.
                                                              (line   6)
* two-sided exponential distribution:    The Laplace Distribution.
                                                              (line   7)
* Type 1 Gumbel distribution, random variates: The Type-1 Gumbel Distribution.
                                                              (line   8)
* Type 2 Gumbel distribution:            The Type-2 Gumbel Distribution.
                                                              (line   8)
* u-transform for series:                Series Acceleration. (line   6)
* underflow, IEEE exceptions:            Setting up your IEEE environment.
                                                              (line   6)
* uniform distribution:                  The Flat (Uniform) Distribution.
                                                              (line   8)
* units, conversion of:                  Physical Constants.  (line   6)
* units, imperial:                       Imperial Units.      (line   6)
* Unix random number generators, rand:   Unix random number generators.
                                                              (line  17)
* Unix random number generators, rand48: Unix random number generators.
                                                              (line  17)
* unnormalized incomplete Gamma function: Incomplete Gamma Functions.
                                                              (line   9)
* unweighted linear fits:                Least-Squares Fitting.
                                                              (line   6)
* usage, compiling application programs: Using the library.   (line   6)
* value function, ntuples:               Histogramming ntuple values.
                                                              (line  24)
* Van der Pol oscillator, example:       ODE Example programs.
                                                              (line   6)
* variance:                              Statistics.          (line   6)
* variance, from histogram:              Histogram Statistics.
                                                              (line  30)
* variance-covariance matrix, linear fits: Fitting Overview.  (line  47)
* VAX random number generator:           Other random number generators.
                                                              (line  87)
* vector, operations:                    BLAS Support.        (line   6)
* vector, sorting elements of:           Sorting vectors.     (line  23)
* vectors <1>:                           Vectors.             (line   6)
* vectors:                               Vectors and Matrices.
                                                              (line   6)
* vectors, initializing:                 Initializing vector elements.
                                                              (line   6)
* vectors, range-checking:               Accessing vector elements.
                                                              (line   6)
* VEGAS Monte Carlo integration:         VEGAS.               (line   6)
* viscosity, units of:                   Viscosity.           (line   6)
* volume units:                          Volume Area and Length.
                                                              (line   6)
* W function:                            Lambert W Functions. (line   6)
* warning options:                       GCC warning options for numerical programs.
                                                              (line   6)
* warranty (none):                       No Warranty.         (line   6)
* wavelet transforms:                    Wavelet Transforms.  (line   6)
* website, developer information:        Further Information. (line   6)
* Weibull distribution:                  The Weibull Distribution.
                                                              (line   8)
* weight, units of:                      Mass and Weight.     (line   6)
* weighted linear fits:                  Least-Squares Fitting.
                                                              (line   6)
* Wigner coefficients:                   Coupling Coefficients.
                                                              (line   6)
* y(x), Bessel Functions:                Irregular Spherical Bessel Functions.
                                                              (line   6)
* Y(x), Bessel Functions:                Irregular Cylindrical Bessel Functions.
                                                              (line   6)
* zero finding:                          One dimensional Root-Finding.
                                                              (line   6)
* zero matrix:                           Initializing matrix elements.
                                                              (line   6)
* zero, IEEE format:                     Representation of floating point numbers.
                                                              (line  27)
* Zeros of Regular Bessel Functions:     Zeros of Regular Bessel Functions.
                                                              (line   6)
* Zeta functions:                        Zeta Functions.      (line   6)
* Ziggurat method:                       The Gaussian Distribution.
                                                              (line  29)