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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 The GSL Team.

   Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.2 or
any later version published by the Free Software Foundation; with the
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 freedom to copy and modify this
GNU Manual, like GNU software."

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

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

* Menu:

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


