 Index Entry   Section 

$   
 $ , shell prompt:   Conventions used in this manual 

2   
 2D histograms:   Two dimensional histograms 
 2D random direction vector:   Spherical Vector Distributions 

3   
 3j symbols:   Coupling Coefficients 
 3D random direction vector:   Spherical Vector Distributions 

6   
 6j symbols:   Coupling Coefficients 

9   
 9j symbols:   Coupling Coefficients 

A   
 acceleration of series:   Series Acceleration 
 acosh:   Elementary Functions 
 Adams method:   Stepping Functions 
 Adaptive stepsize control, differential equations:   Adaptive Stepsize 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, Level1 BLAS:   Level 1 GSL BLAS Interface 
 Angular Mathieu Functions:   Angular Mathieu Functions 
 angular reduction:   Restriction Functions 
 ANSI C, use of:   Using the library 
 Apell symbol, see Pochhammer 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, Level1 BLAS:   Level 1 GSL BLAS Interface 
 atanh:   Elementary Functions 
 atomic physics, constants:   Atomic and Nuclear Physics 
 autoconf, using with GSL:   Autoconf Macros 
 AXPY, Level1 BLAS:   Level 1 GSL BLAS Interface 

B   
 Bspline wavelets:   DWT Initialization 
 Bader and Deuflhard, BulirschStoer method.:   Stepping Functions 
 balancing matrices:   Balancing 
 Basic Linear Algebra Subroutines (BLAS):   BLAS Support 
 Basic Linear Algebra Subroutines (BLAS):   GSL CBLAS Library 
 basis splines, Bsplines:   Basis Splines 
 basis splines, derivatives:   Evaluation of Bspline basis function derivatives 
 basis splines, evaluation:   Evaluation of Bspline basis functions 
 basis splines, examples:   Example programs for Bsplines 
 basis splines, Greville abscissae:   Working with the Greville abscissae 
 basis splines, initializing:   Initializing the Bsplines solver 
 basis splines, MarsdenSchoenberg points:   Working with the Greville abscissae 
 basis splines, overview:   Overview of Bsplines 
 BDF method:   Stepping Functions 
 Bernoulli trial, random variates:   The Bernoulli Distribution 
 Bessel functions:   Bessel Functions 
 Bessel Functions, Fractional Order:   Regular Bessel Function  Fractional Order 
 bestfit 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 algorithm, minimization:   Multimin Algorithms with Derivatives 
 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, Lowlevel 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 
 buggsl mailing list:   Reporting Bugs 
 bugs, how to report:   Reporting Bugs 
 BulirschStoer method:   Stepping Functions 

C   
 C extensions, compatible use of:   Using the library 
 C++, compatibility:   Compatibility with C++ 
 C99, inline keyword:   Inline functions 
 Carlson forms of Elliptic integrals:   Definition of Carlson Forms 
 CashKarp, RungeKutta 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, Lowlevel interface:   GSL CBLAS Library 
 CDFs, cumulative distribution functions:   Random Number Distributions 
 ce(q,x), Mathieu function:   Angular Mathieu Functions 
 Chebyshev series:   Chebyshev Approximations 
 checking combination for validity:   Combination properties 
 checking multiset for validity:   Multiset properties 
 checking permutation for validity:   Permutation properties 
 Chi(x):   Hyperbolic Integrals 
 Chisquared distribution:   The Chisquared Distribution 
 Cholesky decomposition:   Cholesky Decomposition 
 Ci(x):   Trigonometric Integrals 
 Clausen functions:   Clausen Functions 
 ClenshawCurtis 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 FermiDirac integrals:   Complete FermiDirac 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 with Derivatives 
 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, Level1 BLAS:   Level 1 GSL BLAS Interface 
 correlation, of two datasets:   Correlation 
 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 
 cquad, doublyadaptive integration:   CQUAD doublyadaptive integration 
 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 

D   
 Daubechies wavelets:   DWT Initialization 
 Dawson function:   Dawson Function 
 DAXPY, Level1 BLAS:   Level 1 GSL BLAS Interface 
 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, BulirschStoer 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 Ndimensional:   Spherical Vector Distributions 
 Dirichlet distribution:   The Dirichlet Distribution 
 discontinuities, in ODE systems:   Evolution 
 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:   General Discrete Distributions 
 Discrete random numbers:   General Discrete Distributions 
 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, Level1 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   
 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 codes, reserved:   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 
 Eta Function:   Eta Function 
 euclidean distance function, hypot:   Elementary Functions 
 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, C++:   Compatibility with C++ 
 exceptions, floating point:   Handling floating point exceptions 
 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 
 extern inline :   Inline functions 

F   
 Fdistribution:   The Fdistribution 
 factorial:   Factorials 
 factorial:   Factorials 
 factorization of matrices:   Linear Algebra 
 false position algorithm for finding roots:   Root Bracketing Algorithms 
 Fast Fourier Transforms, see FFT:   Fast Fourier Transforms 
 Fehlberg method, differential equations:   Stepping Functions 
 FermiDirac function:   FermiDirac Function 
 FFT:   Fast Fourier Transforms 
 FFT mathematical definition:   Mathematical Definitions 
 FFT of complex data, mixedradix algorithm:   Mixedradix FFT routines for complex data 
 FFT of complex data, radix2 algorithm:   Radix2 FFT routines for complex data 
 FFT of real data:   Overview of real data FFTs 
 FFT of real data, mixedradix algorithm:   Mixedradix FFT routines for real data 
 FFT of real data, radix2 algorithm:   Radix2 FFT routines for real data 
 FFT, complex data:   Overview of complex data FFTs 
 finding minima:   One dimensional Minimization 
 finding roots:   One dimensional RootFinding 
 finding zeros:   One dimensional RootFinding 
 fits, multiparameter linear:   Multiparameter fitting 
 fitting:   LeastSquares Fitting 
 fitting, using Chebyshev polynomials:   Chebyshev Approximations 
 Fj(x), FermiDirac integral:   Complete FermiDirac Integrals 
 Fj(x,b), incomplete FermiDirac integral:   Incomplete FermiDirac Integrals 
 flat distribution:   The Flat (Uniform) Distribution 
 FletcherReeves conjugate gradient algorithm, minimization:   Multimin Algorithms with Derivatives 
 floating point exceptions:   Handling floating point exceptions 
 floating point numbers, approximate comparison:   Approximate Comparison of Floating Point Numbers 
 floating point registers:   Examining floating point registers 
 force and energy, units of:   Force and Energy 
 Fortran range checking, equivalent in gcc:   Accessing vector elements 
 Fourtap 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 software, explanation of:   GSL is Free Software 
 frexp:   Elementary Functions 
 functions, numerical differentiation:   Numerical Differentiation 
 fundamental constants:   Fundamental Constants 

G   
 Gamma distribution:   The Gamma Distribution 
 gamma functions:   Gamma Functions 
 GaussKronrod 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, rangechecking:   Accessing vector elements 
 gcc warning options:   GCC warning options for numerical programs 
 gdb:   Using gdb 
 Gegenbauer functions:   Gegenbauer Functions 
 GEMM, Level3 BLAS:   Level 3 GSL BLAS Interface 
 GEMV, Level2 BLAS:   Level 2 GSL BLAS Interface 
 general polynomial equations, solving:   General Polynomial Equations 
 generalized eigensystems:   Real Generalized Nonsymmetric Eigensystems 
 generalized hermitian definite eigensystems:   Complex Generalized HermitianDefinite Eigensystems 
 generalized symmetric eigensystems:   Real Generalized SymmetricDefinite Eigensystems 
 Geometric random variates:   The Geometric Distribution 
 Geometric random variates:   The Hypergeometric Distribution 
 GER, Level2 BLAS:   Level 2 GSL BLAS Interface 
 GERC, Level2 BLAS:   Level 2 GSL BLAS Interface 
 GERU, Level2 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_C99_INLINE:   Inline functions 
 GSL_RNG_SEED :   Random number generator initialization 
 gsl_sf_result:   The gsl_sf_result struct 
 gsl_sf_result_e10:   The gsl_sf_result struct 
 Gumbel distribution (Type 1):   The Type1 Gumbel Distribution 
 Gumbel distribution (Type 2):   The Type2 Gumbel Distribution 

H   
 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, Level3 BLAS:   Level 3 GSL BLAS Interface 
 HEMV, Level2 BLAS:   Level 2 GSL BLAS Interface 
 HER, Level2 BLAS:   Level 2 GSL BLAS Interface 
 HER2, Level2 BLAS:   Level 2 GSL BLAS Interface 
 HER2K, Level3 BLAS:   Level 3 GSL BLAS Interface 
 HERK, Level3 BLAS:   Level 3 GSL BLAS Interface 
 hermitian matrix, complex, eigensystem:   Complex Hermitian Matrices 
 Hessenberg decomposition:   Hessenberg Decomposition of Real Matrices 
 Hessenberg triangular decomposition:   HessenbergTriangular Decomposition of Real 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 
 Hurwitz Zeta Function:   Hurwitz Zeta Function 
 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 

I   
 I(x), Bessel Functions:   Regular Modified Cylindrical Bessel Functions 
 i(x), Bessel Functions:   Regular Modified Spherical Bessel Functions 
 identity matrix:   Initializing matrix elements 
 identity permutation:   Permutation allocation 
 IEEE exceptions:   Setting up your IEEE environment 
 IEEE floating point:   IEEE floatingpoint arithmetic 
 IEEE format for floating point numbers:   Representation of floating point numbers 
 IEEE infinity, defined as a macro:   Infinities and Notanumber 
 IEEE NaN, defined as a macro:   Infinities and Notanumber 
 illumination, units of:   Light and Illumination 
 imperial units:   Imperial Units 
 Implicit Euler method:   Stepping Functions 
 Implicit RungeKutta method:   Stepping Functions 
 importance sampling, VEGAS:   VEGAS 
 including GSL header files:   Compiling and Linking 
 incomplete Beta function, normalized:   Incomplete Beta Function 
 incomplete FermiDirac integral:   Incomplete FermiDirac 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 Notanumber 
 infinity, IEEE format:   Representation of floating point numbers 
 infogsl 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 multisets:   Multiset functions 
 iterating through permutations:   Permutation functions 
 iterative refinement of solutions in linear systems:   LU Decomposition 

J   
 J(x), Bessel Functions:   Regular Cylindrical Bessel Functions 
 j(x), Bessel Functions:   Regular Spherical Bessel Functions 
 Jacobi elliptic functions:   Elliptic Functions (Jacobi) 
 Jacobi orthogonalization:   Singular Value Decomposition 
 Jacobian matrix, fitting:   Overview of Nonlinear LeastSquares Fitting 
 Jacobian matrix, ODEs:   Defining the ODE System 
 Jacobian matrix, root finding:   Overview of Multidimensional Root Finding 

K   
 K(x), Bessel Functions:   Irregular Modified Cylindrical Bessel Functions 
 k(x), Bessel Functions:   Irregular Modified Spherical Bessel Functions 
 knots, basis splines:   Constructing the knots vector 
 kurtosis:   Higher moments (skewness and kurtosis) 

L   
 Laguerre functions:   Laguerre Functions 
 Lambert function:   Lambert W Functions 
 Landau distribution:   The Landau Distribution 
 LAPACK:   Eigenvalue and Eigenvector References 
 Laplace distribution:   The Laplace Distribution 
 ldexp:   Elementary Functions 
 LD_LIBRARY_PATH:   Shared Libraries 
 leading dimension, matrices:   Matrices 
 least squares fit:   LeastSquares Fitting 
 least squares fitting, nonlinear:   Nonlinear LeastSquares Fitting 
 least squares troubleshooting:   Troubleshooting 
 least squares, covariance of bestfit 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 
 Legendre polynomials:   Legendre Functions and Spherical Harmonics 
 length, computed accurately using hypot:   Elementary Functions 
 length, computed accurately using hypot:   Elementary Functions 
 LevenbergMarquardt algorithms:   Minimization Algorithms using Derivatives 
 Levin utransform:   Series Acceleration 
 Levy distribution:   The Levy alphaStable Distributions 
 Levy distribution, skew:   The Levy skew alphaStable 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:   QuasiRandom Sequences 
 Lowlevel CBLAS:   GSL CBLAS Library 
 LU decomposition:   LU Decomposition 

M   
 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, buggsl:   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 
 Mathieu Function Characteristic Values:   Mathieu Function Characteristic Values 
 Mathieu functions:   Mathieu Functions 
 matrices:   Vectors and Matrices 
 matrices:   Matrices 
 matrices, initializing:   Initializing matrix elements 
 matrices, rangechecking:   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 
 Mills’ ratio, inverse:   Probability functions 
 min:   Statistics 
 minimization, BFGS algorithm:   Multimin Algorithms with Derivatives 
 minimization, caveats:   Minimization Caveats 
 minimization, conjugate gradient algorithm:   Multimin Algorithms with Derivatives 
 minimization, multidimensional:   Multidimensional Minimization 
 minimization, onedimensional:   One dimensional Minimization 
 minimization, overview:   Minimization Overview 
 minimization, PolakRibiere algorithm:   Multimin Algorithms with Derivatives 
 minimization, providing a function to minimize:   Providing the function to minimize 
 minimization, simplex algorithm:   Multimin Algorithms without Derivatives 
 minimization, steepest descent algorithm:   Multimin Algorithms with Derivatives 
 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:   Algorithms using Derivatives 
 MINPACK, minimization algorithms:   Minimization Algorithms using Derivatives 
 MISCFUN:   Special Functions References and Further Reading 
 MISER monte carlo integration:   MISER 
 Mixedradix FFT, complex data:   Mixedradix FFT routines for complex data 
 Mixedradix FFT, real data:   Mixedradix FFT routines for real data 
 Modified Bessel Functions, Fractional Order:   Regular Modified Bessel Functions  Fractional Order 
 Modified ClenshawCurtis 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 
 multiparameter regression:   Multiparameter fitting 
 multidimensional integration:   Monte Carlo Integration 
 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 
 multisets:   Multisets 
 multistep methods, ODEs:   Stepping Functions 

N   
 Ndimensional random direction vector:   Spherical Vector Distributions 
 NaN, defined as a macro:   Infinities and Notanumber 
 nautical units:   Speed and Nautical Units 
 Negative Binomial distribution, random variates:   The Negative Binomial Distribution 
 NelderMead simplex algorithm for minimization:   Multimin Algorithms without Derivatives 
 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:   QuasiRandom Sequences 
 NIST Statistical Reference Datasets:   Fitting References and Further Reading 
 nonnormalized incomplete Gamma function:   Incomplete Gamma Functions 
 nonlinear equation, solutions of:   One dimensional RootFinding 
 nonlinear fitting, stopping parameters:   Search Stopping Parameters for Minimization Algorithms 
 nonlinear functions, minimization:   One dimensional Minimization 
 nonlinear least squares fitting:   Nonlinear LeastSquares Fitting 
 nonlinear least squares fitting, overview:   Overview of Nonlinear LeastSquares Fitting 
 nonlinear systems of equations, solution of:   Multidimensional RootFinding 
 nonsymmetric matrix, real, eigensystem:   Real Nonsymmetric Matrices 
 Nordsieck form:   Stepping Functions 
 normalized form, IEEE format:   Representation of floating point numbers 
 normalized incomplete Beta function:   Incomplete Beta Function 
 Notanumber, defined as a macro:   Infinities and Notanumber 
 NRM2, Level1 BLAS:   Level 1 GSL BLAS Interface 
 ntuples:   Ntuples 
 nuclear physics, constants:   Atomic and Nuclear Physics 
 numerical constants, defined as macros:   Mathematical Constants 
 numerical derivatives:   Numerical Differentiation 
 numerical integration (quadrature):   Numerical Integration 

O   
 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 
 ordering, matrix elements:   Matrices 
 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 

P   
 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 
 PolakRibiere algorithm, minimization:   Multimin Algorithms with Derivatives 
 polar form of complex numbers:   Representation of 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 
 predictorcorrector method, ODEs:   Stepping Functions 
 prefixes:   Prefixes 
 pressure, units of:   Pressure 
 PrinceDormand, RungeKutta 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 

Q   
 QAG quadrature algorithm:   QAG adaptive integration 
 QAGI quadrature algorithm:   QAGI adaptive integration on infinite intervals 
 QAGP quadrature algorithm:   QAGP adaptive integration with known singular points 
 QAGS quadrature algorithm:   QAGS adaptive integration with singularities 
 QAWC quadrature algorithm:   QAWC adaptive integration for Cauchy principal values 
 QAWF quadrature algorithm:   QAWF adaptive integration for Fourier integrals 
 QAWO quadrature algorithm:   QAWO adaptive integration for oscillatory functions 
 QAWS quadrature algorithm:   QAWS adaptive integration for singular functions 
 QNG quadrature algorithm:   QNG nonadaptive GaussKronrod integration 
 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 
 quasirandom sequences:   QuasiRandom Sequences 

R   
 R250 shiftregister random number generator:   Other random number generators 
 Racah coefficients:   Coupling Coefficients 
 Radial Mathieu Functions:   Radial Mathieu Functions 
 radioactivity, units of:   Radioactivity 
 Radix2 FFT for real data:   Radix2 FFT routines for real data 
 Radix2 FFT, complex data:   Radix2 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 
 rangechecking for matrices:   Accessing matrix elements 
 rangechecking 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 
 RANMAR random number generator:   Other random number generators 
 Rayleigh distribution:   The Rayleigh Distribution 
 Rayleigh Tail distribution:   The Rayleigh Tail Distribution 
 real nonsymmetric matrix, eigensystem:   Real Nonsymmetric Matrices 
 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:   LeastSquares 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:   Representation of complex numbers 
 resampling from histograms:   Resampling from histograms 
 residual, in nonlinear systems of equations:   Search Stopping Parameters for the multidimensional solver 
 residual, in nonlinear systems of equations:   Search Stopping Parameters for Minimization Algorithms 
 reversing a permutation:   Permutation functions 
 Riemann Zeta Function:   Riemann Zeta Function 
 RK2, RungeKutta method:   Stepping Functions 
 RK4, RungeKutta method:   Stepping Functions 
 RKF45, RungeKuttaFehlberg method:   Stepping Functions 
 robust regression:   Robust linear regression 
 root finding:   One dimensional RootFinding 
 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:   Search Stopping Parameters 
 root finding, stopping parameters:   Search Stopping Parameters for the multidimensional solver 
 roots:   One dimensional RootFinding 
 ROTG, Level1 BLAS:   Level 1 GSL BLAS Interface 
 rounding mode:   Setting up your IEEE environment 
 RungeKutta CashKarp method:   Stepping Functions 
 RungeKutta methods, ordinary differential equations:   Stepping Functions 
 RungeKutta PrinceDormand method:   Stepping Functions 

S   
 safe comparison of floating point numbers:   Approximate Comparison of Floating Point Numbers 
 safeguarded steplength algorithm:   Minimization Algorithms 
 sampling from histograms:   Resampling from histograms 
 sampling from histograms:   The histogram probability distribution struct 
 SAXPY, Level1 BLAS:   Level 1 GSL BLAS Interface 
 SCAL, Level1 BLAS:   Level 1 GSL BLAS Interface 
 schedule, cooling:   Simulated Annealing algorithm 
 se(q,x), Mathieu function:   Angular Mathieu Functions 
 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 
 shiftregister 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 without Derivatives 
 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 alphaStable Distribution 
 skewness:   Higher moments (skewness and kurtosis) 
 slope, see numerical derivative:   Numerical Differentiation 
 Sobol sequence:   QuasiRandom 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 RootFinding 
 solving nonlinear systems of equations:   Multidimensional RootFinding 
 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, Ndimensional:   Spherical Vector Distributions 
 spline:   Interpolation 
 splines, basis:   Basis Splines 
 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 with Derivatives 
 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 tdistribution:   The tdistribution 
 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, Level1 BLAS:   Level 1 GSL BLAS Interface 
 swapping permutation elements:   Accessing permutation elements 
 SYMM, Level3 BLAS:   Level 3 GSL BLAS Interface 
 symmetric matrix, real, eigensystem:   Real Symmetric Matrices 
 SYMV, Level2 BLAS:   Level 2 GSL BLAS Interface 
 synchrotron functions:   Synchrotron Functions 
 SYR, Level2 BLAS:   Level 2 GSL BLAS Interface 
 SYR2, Level2 BLAS:   Level 2 GSL BLAS Interface 
 SYR2K, Level3 BLAS:   Level 3 GSL BLAS Interface 
 SYRK, Level3 BLAS:   Level 3 GSL BLAS Interface 
 systems of equations, nonlinear:   Multidimensional RootFinding 

T   
 tdistribution:   The tdistribution 
 ttest:   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 multiset for validity:   Multiset 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:   Tridiagonal Decomposition of Real Symmetric Matrices 
 tridiagonal decomposition:   Tridiagonal Decomposition of Hermitian Matrices 
 tridiagonal systems:   Tridiagonal Systems 
 trigonometric functions:   Trigonometric Functions 
 trigonometric functions of complex numbers:   Complex Trigonometric Functions 
 trigonometric integrals:   Trigonometric Integrals 
 TRMM, Level3 BLAS:   Level 3 GSL BLAS Interface 
 TRMV, Level2 BLAS:   Level 2 GSL BLAS Interface 
 TRSM, Level3 BLAS:   Level 3 GSL BLAS Interface 
 TRSV, Level2 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 
 twosided exponential distribution:   The Laplace Distribution 
 Type 1 Gumbel distribution, random variates:   The Type1 Gumbel Distribution 
 Type 2 Gumbel distribution:   The Type2 Gumbel Distribution 

U   
 utransform 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:   LeastSquares Fitting 
 usage, compiling application programs:   Using the library 

V   
 value function, ntuples:   Histogramming ntuple values 
 Van der Pol oscillator, example:   ODE Example programs 
 variance:   Statistics 
 variance, from histogram:   Histogram Statistics 
 variancecovariance matrix, linear fits:   Fitting Overview 
 VAX random number generator:   Other random number generators 
 vector, operations:   BLAS Support 
 vector, sorting elements of:   Sorting vectors 
 vectors:   Vectors and Matrices 
 vectors:   Vectors 
 vectors, initializing:   Initializing vector elements 
 vectors, rangechecking:   Accessing vector elements 
 VEGAS Monte Carlo integration:   VEGAS 
 viscosity, units of:   Viscosity 
 volume units:   Volume Area and Length 

W   
 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:   LeastSquares Fitting 
 Wigner coefficients:   Coupling Coefficients 

Y   
 Y(x), Bessel Functions:   Irregular Cylindrical Bessel Functions 
 y(x), Bessel Functions:   Irregular Spherical Bessel Functions 

Z   
 zero finding:   One dimensional RootFinding 
 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 
 Ziggurat method:   The Gaussian Distribution 
