GSL - Definition and Overview

GNU Scientific Library is a library in the C language for mathematics and science, distributed under the GNU GPL.

It provides facilities for:

• Basic Mathematical Functions
• Complex Numbers
• Polynomials
• Special functions
  • Airy functions and derivatives
    • Airy functions
    • Derivatives of Airy functions
    • Zeros of Airy functions
    • Zeros of derivatives of Airy functions
  • Bessel functions
    • Regular cylindrical Bessel functions
    • Irregular cylindrical Bessel functions
    • Regular modified cylindrical Bessel functions
    • Irregular modified cylindrical Bessel functions
    • Regular spherical Bessel functions
    • Irregular spherical Bessel functions
    • Regular modified spherical Bessel functions
    • Irregular modified spherical Bessel functions
    • Regular Bessel function - fractional order
    • Irregular Bessel functions - fractional order
    • Regular modified Bessel functions - fractional order
    • Irregular modified Bessel functions - fractional order
    • Zeros of regular Bessel functions
  • Clausen functions
  • Coulomb functions
    • Normalized hydrogenic bound states
    • Coulomb wave functions
    • Coulomb wave function normalization constant
  • Coupling coefficients
    • 3-j symbols
    • 6-j symbols
    • 9-j symbols
  • Dawson function
  • Debye functions
  • Dilogarithm
  • Elementary operations
  • Elliptic integrals
    • Definition of Legendre forms
    • Definition of Carlson forms
    • Legendre form of complete elliptic integrals
    • Legendre form of incomplete elliptic integrals
    • Carlson forms
  • Elliptic functions (Jacobi)
  • Error functions
    • Error function
    • Complementary error function
    • Log complementary error function
    • Probability functions
  • Exponential functions
    • Exponential function
    • Relative exponential functions
    • Exponentiation with error estimate
  • Exponential integrals
    • Exponential integral
    • Ei(x)
    • Hyperbolic integrals
    • Ei_3(x)
    • Trigonometric integrals
    • Arctangent integral
  • Fermi-Dirac function
    • Complete Fermi-Dirac integrals
    • Incomplete Fermi-Dirac integrals
  • Gamma function
  • Gegenbauer functions
  • Hypergeometric functions
  • Laguerre functions
  • Lambert W functions
  • Legendre functions and spherical harmonics
    • Legendre polynomials
    • Associated Legendre polynomials and spherical harmonics
    • Conical functions
    • Radial functions for hyperbolic space
  • Logarithm and related functions
  • Power function
  • Psi (Digamma) function
    • Digamma function
    • Trigamma function
    • Polygamma function
  • Synchrotron functions
  • Transport functions
  • Trigonometric functions
    • Circular Trigonometric functions
    • Trigonometric functions for complex arguments
    • Hyperbolic Trigonometric functions
    • Conversion functions
    • Restriction functions
    • Trigonometric functions with error estimates
  • Zeta functions
    • Riemann Zeta function
    • Riemann Zeta function minus one
    • Hurwitz Zeta function
    • Eta function
• Vectors and Matrices
• Permutations
• Combinations
• Sorting
• BLAS
• Linear Algebra
• Eigensystems
• Fast Fourier Transforms
• Numerical Integration
• Random Number Generation
• Quasi-Random Sequences
• Random Number Distributions
  • Gaussian distribution
  • Gaussian tail distribution
  • Bivariate Gaussian distribution
  • Exponential distribution
  • Laplace distribution
  • Exponential power distribution
  • Cauchy distribution
  • Rayleigh distribution
  • Rayleigh tail distribution
  • Landau distribution
  • Levy alpha-stable distributions
  • Levy skew alpha-stable distribution
  • Gamma distribution
  • Flat (Uniform) distribution
  • Lognormal distribution
  • Chi-squared distribution
  • F-distribution
  • t-distribution
  • Beta distribution
  • Logistic distribution
  • Pareto distribution
  • Spherical vector distributions
  • Weibull distribution
  • Type-1 Gumbel distribution
  • Type-2 Gumbel distribution
  • Dirichlet distribution
  • General discrete distributions
  • Poisson distribution
  • Bernoulli distribution
  • Binomial distribution
  • Multinomial distribution
  • Negative binomial distribution
  • Pascal distribution
  • Geometric distribution
  • Hypergeometric distribution
  • Logarithmic distribution
• Statistics
• Histograms
• N-tuples
• Monte Carlo Integration
• Simulated Annealing
• Ordinary Differential Equations
• Interpolation
• Numerical differentiation
• Chebyshev approximations
• Series acceleration
• Discrete Hankel Transforms
• One dimensional Root-Finding
• One dimensional minimization
• Multidimensional Root-Finding
• Multidimensional minimization
• Least-Squares Fitting
• Nonlinear Least-Squares Fitting
• Physical constants
• IEEE floating-point arithmetic

Its manual is available at http://www.gnu.org/software/gsl/manual/gsl-ref_toc.html. Being released under the GFDL, its contents may be used as the basis of Wikipedia articles.