http://sourceware.cygnus.com/gsl/

What is gsl?

   The GNU Scientific Library (GSL) is a collection of routines for numerical
   computing. The routines are written from scratch by the GSL team in ANSI
   C, and are meant to present a modern Applications Programming Interface
   (API) for C programmers, while allowing wrappers to be written for very
   high level languages.

As of 3 December 1999, the complete packages are the random number suite (see
section [[Random Number Generation]]), the quadrature package (see section
[[Numerical Integration]]), the FFT package (see section [[Fast Fourier
Transforms (FFTs)]]), the simulated annealing package (see section [[Simulated
Annealing]]) and the root finding package (see section [[Solutions of
Nonlinear Equations]]). Work is under way on a special function library.

   o [[Preliminaries]]
   o [[Using the library]]
        o [[ Compiling and Linking]]
        o [[Inline functions]]
        o [[Long double]]
        o [[Alternative optimized functions]]
   o [[Error handling in GSL]]
        o [[ Error reporting]]
        o [[Error handlers]]
        o [[Error streams]]
        o [[Manipulating the error stream]]
        o [[Using GSL error reporting in your own functions]]
   o [[Random Number Generation]]
        o [[ General comments on random numbers]]
        o [[The Random Number Generator Interface]]
        o [[Random number generator initialization]]
        o [[Sampling from a random number generator]]
        o [[Auxiliary random number generator functions]]
        o [[Random number environment variables]]
        o [[Saving and restoring random number generator state]]
        o [[Available random number generator algorithms]]
             o [[ Simulation quality generators]]
             o [[Unix random number generators]]
             o [[Numerical Recipes generators]]
             o [[Other random number generators]]
        o [[Random Number Generator Performance]]
        o [[References and Further Reading]]
        o [[Acknowledgements]]
   o [[Random Number Distributions]]
        o [[ The Gaussian Distribution]]
        o [[The Gaussian Tail Distribution]]
        o [[The Bivariate Gaussian Distribution]]
        o [[The Exponential Distribution]]
        o [[The Laplace Distribution]]
        o [[The Exponential Power Distribution]]
        o [[The Cauchy Distribution]]
        o [[The Rayleigh Distribution]]
        o [[The Rayleigh Tail Distribution]]
        o [[The Symmetric Levy Distribution]]
        o [[The Gamma Distribution]]
        o [[The Flat (Uniform) Distribution]]
        o [[The Lognormal Distribution]]
        o [[The Chi-squared Distribution]]
        o [[The F-distribution]]
        o [[The t-distribution]]
        o [[The Beta Distribution]]
        o [[The Logistic Distribution]]
        o [[The Pareto Distribution]]
        o [[The Spherical Distribution (2D & 3D)]]
        o [[The Weibull Distribution]]
        o [[The Type-1 Gumbel Distribution]]
        o [[The Type-2 Gumbel Distribution]]
        o [[General Discrete Distributions]]
        o [[The Poisson Distribution]]
        o [[The Bernoulli Distribution]]
        o [[The Binomial Distribution]]
        o [[The Negative Binomial Distribution]]
        o [[The Geometric Distribution]]
        o [[The Hypergeometric Distribution]]
        o [[The Logarithmic Distribution]]
        o [[Shuffling and Sampling]]
        o [[Examples]]
        o [[References and Further Reading]]
   o [[Statistics]]
        o [[ Mean, Standard Deviation and Variance]]
        o [[Absolute deviation]]
        o [[Higher moments (skewness and kurtosis)]]
        o [[Maximum and Minimum values]]
        o [[Median and Percentiles]]
        o [[Statistical tests]]
        o [[Example statistical programs]]
        o [[References and Further Reading]]
   o [[Fast Fourier Transforms (FFTs)]]
        o [[ Mathematical Definitions]]
        o [[Overview of complex data FFTs]]
        o [[Radix-2 FFT routines for complex data]]
        o [[Mixed-radix FFT routines for complex data]]
        o [[Overview of real data FFTs]]
        o [[Radix-2 FFT routines for real data]]
        o [[Mixed-radix FFT routines for real data]]
        o [[References and Further Reading]]
   o [[Roots of Polynomials]]
        o [[ Quadratic equations]]
        o [[Cubic equations]]
        o [[General polynomial equations]]
        o [[Examples]]
        o [[References and Further Reading]]
   o [[Solutions of Nonlinear Equations]]
        o [[ Overview]]
        o [[Caveats]]
        o [[Initializing the Solver]]
        o [[Providing the function to solve]]
        o [[Search Bounds and Guesses]]
        o [[Iteration]]
        o [[Search Stopping Parameters]]
        o [[Root Bracketing Algorithms]]
        o [[Root Finding Algorithms using Derivatives]]
        o [[Examples]]
        o [[References and Further Reading]]
   o [[Solutions of Multidimensional Nonlinear Equations]]
        o [[ Overview]]
        o [[Initializing the Solver]]
        o [[Providing the function to solve]]
        o [[Iteration]]
        o [[Search Stopping Parameters]]
        o [[Root Finding Algorithms without derivatives]]
        o [[Multidimensional Root Finding Algorithms using Derivatives]]
        o [[References and Further Reading]]
   o [[Minimization]]
        o [[ Overview]]
        o [[Caveats]]
        o [[Initializing the Minimizer]]
        o [[Providing the function to minimize]]
        o [[Iteration]]
        o [[Stopping Parameters]]
        o [[Minimization Algorithms]]
        o [[Examples]]
        o [[References and Further Reading]]
   o [[Special Functions]]
        o [[ The gsl_sf_result struct]]
        o [[Airy Functions]]
             o [[ Airy Functions]]
             o [[Derivatives of Airy Functions]]
             o [[Zeros of Airy Functions]]
             o [[Zeros of Derivatives of Airy Functions]]
        o [[Bessel Functions]]
             o [[ Regular Cylindrical Bessel Functions]]
             o [[Irregular Cylindrical Bessel Functions]]
             o [[Regular Modified Cylindrical Bessel Functions]]
             o [[Irregular Modified Cylindrical Bessel Functions]]
             o [[Regular Spherical Bessel Functions]]
             o [[Irregular Spherical Bessel Functions]]
             o [[Regular Modified Spherical Bessel Functions]]
             o [[Irregular Modified Spherical Bessel Functions]]
             o [[Regular Bessel Function, Fractional Order]]
             o [[Irregular Bessel Functions, Fractional Order]]
             o [[Regular Modified Bessel Functions, Fractional Order]]
             o [[Irregular Modified Bessel Functions, Fractional Order]]
             o [[Zeros of Regular Bessel Functions]]
        o [[Chebyshev Polynomials]]
             o [[ The gsl_sf_cheb_series struct]]
             o [[Creation/Calculation of Chebyshev Series]]
             o [[Chebyshev Series Evaluation]]
             o [[Delete a Chebyshev Expansion]]
        o [[Clausen Functions]]
        o [[Coulomb Wave Functions]]
             o [[ Normalized Hydrogenic Bound States]]
             o [[Coulomb Wave Functions]]
             o [[Coulomb Wave Function Normalization Constant]]
        o [[Coupling Coefficients]]
             o [[ 3j Symbols]]
             o [[6j Symbols]]
             o [[9j Symbols]]
        o [[Dawson Function]]
        o [[Debye Functions]]
        o [[Dilogarithm]]
             o [[ Real Argument]]
             o [[Complex Argument]]
        o [[Elementary Operations]]
        o [[Elliptic Integrals]]
             o [[ Legendre Forms]]
             o [[Carlson Forms]]
             o [[Legendre Form of Complete Elliptic Integrals]]
             o [[Legendre Form of Incomplete Elliptic Integrals]]
             o [[Carlson Forms]]
        o [[Elliptic Functions (Jacobi)]]
        o [[Error Function]]
             o [[ Complementary Error Function]]
             o [[Log Complementary Error Function]]
             o [[Error Function]]
             o [[Probability functions]]
        o [[Exponential Function]]
             o [[ Exponential Function]]
             o [[Relative Exponential Functions]]
             o [[Exponentiation With Error Estimate]]
        o [[Exponential Integrals]]
             o [[ Exponential Integrals]]
             o [[Ei(x)]]
             o [[Hyperbolic Integrals]]
             o [[Ei_3(x)]]
             o [[Trigonometric Integrals]]
             o [[Arctangent Integral]]
        o [[Fermi-Dirac Function]]
             o [[ Complete Fermi-Dirac Integrals]]
             o [[Incomplete Fermi-Dirac Integrals:]]
        o [[Gamma Function]]
        o [[Gegenbauer Functions]]
        o [[Hypergeometric Functions]]
        o [[Laguerre Functions]]
        o [[Legendre Functions and Spherical Harmonics]]
             o [[ Legendre Polynomials]]
             o [[Associated Legendre Polynomials and Spherical Harmonics]]
             o [[Conical Functions]]
             o [[Radial Functions for Hyperbolic Space]]
        o [[Logarithm and Related Functions]]
        o [[Polynomial Manipulation]]
        o [[Power Function]]
        o [[Psi (Digamma) Function]]
             o [[ Digamma Function]]
             o [[Trigamma Function]]
             o [[Polygamma Function]]
        o [[Synchrotron Functions]]
        o [[Transport Functions]]
        o [[Trigonometric Functions]]
             o [[ Trigonometric Functions]]
             o [[Conversion Functions]]
             o [[Restriction Functions]]
        o [[Zeta Functions]]
             o [[ Riemann Zeta Function]]
             o [[Hurwicz Zeta Function]]
             o [[Eta Function]]
   o [[Discrete Hankel Transforms]]
   o [[Interpolation]]
        o [[ Introduction]]
        o [[Functions]]
        o [[Examples]]
             o [[ Creating and Using a Linear Interpolation]]
             o [[Creating and Using Other Interpolations]]
   o [[Series Acceleration]]
        o [[ Acceleration functions]]
        o [[Example of accelerating a series]]
        o [[References and Further Reading]]
   o [[Simulated Annealing]]
        o [[ Simulated Annealing algorithm]]
        o [[Simulated Annealing functions]]
        o [[Examples with Simulated Annealing]]
             o [[ Trivial example]]
             o [[Traveling Salesman Problem]]
   o [[Vectors and Matrices]]
        o [[ Data types]]
        o [[The block struct]]
        o [[Block allocation]]
        o [[Reading and writing blocks]]
        o [[Example programs for blocks]]
        o [[The vector struct]]
        o [[Vector allocation]]
        o [[Accessing vector elements]]
        o [[Reading and writing vectors]]
        o [[Copying vectors]]
        o [[Exchanging elements]]
        o [[Vector properties]]
        o [[Example programs for vectors]]
        o [[The matrix struct]]
        o [[Matrix allocation]]
        o [[Accessing matrix elements]]
        o [[Reading and writing matrices]]
        o [[Slicing rows and columns]]
        o [[Copying matrices]]
        o [[Copying rows and columns]]
        o [[Exchanging rows and columns]]
        o [[Example programs for matrices]]
   o [[BLAS Support]]
        o [[ Introduction]]
        o [[Organization]]
        o [[GSL BLAS Interface]]
        o [[Raw BLAS Interface]]
        o [[References and Further Reading]]
   o [[Linear Algebra]]
        o [[ Singular Value Decomposition]]
        o [[LU Decomposition]]
        o [[QR Decomposition]]
        o [[Tridiagonal Systems]]
        o [[References and Further Reading]]
   o [[Eigensystems]]
   o [[Histograms]]
        o [[ The histogram struct]]
        o [[Histogram allocation]]
        o [[Updating and accessing histogram elements]]
        o [[Searching histogram ranges]]
        o [[Reading and writing histograms]]
        o [[Resampling from histograms]]
        o [[The histogram probability distribution struct]]
        o [[Example programs for histograms]]
        o [[Two dimensional histograms]]
        o [[The 2D histogram struct]]
        o [[2D Histogram allocation]]
        o [[Updating and accessing 2D histogram elements]]
        o [[Searching 2D histogram ranges]]
        o [[Reading and writing 2D histograms]]
        o [[Resampling from 2D histograms]]
        o [[Example programs for 2D histograms]]
   o [[Numerical Integration]]
        o [[ QNG non-adaptive Gauss-Kronrod integration]]
        o [[QAG adaptive integration]]
        o [[QAGS adaptive integration with singularities]]
        o [[QAGP adaptive integration with known singular points]]
        o [[QAGI adaptive integration on infinite intervals]]
        o [[QAWC adaptive integration for Cauchy principal values]]
        o [[QAWS adaptive integration for singular functions]]
        o [[QAWO adaptive integration for oscillatory functions]]
        o [[QAWF adaptive integration for Fourier integrals]]
        o [[Error codes]]
        o [[Examples]]
        o [[References and Further Reading]]
   o [[Monte Carlo Integration]]
        o [[ Algorithms]]
             o [[ PLAIN (or Simple) Monte Carlo]]
             o [[MISER]]
             o [[VEGAS]]
        o [[Interface]]
        o [[Example]]
        o [[The Future]]
   o [[Ordinary Differential Equations (ODEs)]]
   o [[The IEEE standard for floating-point arithmetic]]
        o [[ Representation of floating point numbers]]
        o [[Setting up your IEEE environment]]
        o [[References and Further Reading]]
   o [[Debugging Numerical Programs]]
        o [[ Using gdb]]
        o [[GCC warning options for numerical programs]]
   o [[Contributors to GSL]]
   o [[Copying]]
   o [[Concept Index]]
   o [[Function Index]]
   o [[Variable Index]]
   o [[Type Index]]