# Special Functions

This chapter describes the GSL special function library. The library includes routines for calculating the values of Airy functions, Bessel functions, Clausen functions, Coulomb wave functions, Coupling coefficients, the Dawson function, Debye functions, Dilogarithms, Elliptic integrals, Jacobi elliptic functions, Error functions, Exponential integrals, Fermi-Dirac functions, Gamma functions, Gegenbauer functions, Hypergeometric functions, Laguerre functions, Legendre functions and Spherical Harmonics, the Psi (Digamma) Function, Synchrotron functions, Transport functions, Trigonometric functions and Zeta functions. Each routine also computes an estimate of the numerical error in the calculated value of the function.

The functions are declared in individual header files, such as ``gsl_sf_airy.h'`, ``gsl_sf_bessel.h'`, etc. The complete set of header files can be included using the file ``gsl_sf.h'`.

- Special Function Usage
- The gsl_sf_result struct
- Special Function Modes
- Airy Functions and Derivatives
- Bessel Functions
- Clausen Functions
- Coulomb Functions
- Coupling Coefficients
- Dawson Function
- Debye Functions
- Dilogarithm
- Elementary Operations
- Elliptic Integrals
- Elliptic Functions (Jacobi)
- Error Functions
- Exponential Functions
- Exponential Integrals
- Fermi-Dirac Function
- Gamma Function
- Gegenbauer Functions
- Hypergeometric Functions
- Laguerre Functions
- Lambert W Functions
- Legendre Functions and Spherical Harmonics
- Logarithm and Related Functions
- Power Function
- Psi (Digamma) Function
- Synchrotron Functions
- Transport Functions
- Trigonometric Functions
- Zeta Functions
- Special Functions Examples
- Special Functions References and Further Reading