Special Functions

TOMS715 is a FORTRAN90 library which evaluates special functions, including the Bessel I, J, K, and Y functions of order 0, of order 1, and of any real order, Dawson's integral, the error function, exponential integrals, the gamma function, the normal distribution function, the psi function. This is a version of ACM TOMS algorithm 715.


The computer code and data files made available on this web page are distributed under the GNU LGPL license.


TOMS715 is available in a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

FN, a FORTRAN90 library which approximates elementary and special functions using Chebyshev polynomials; functions include Airy, Bessel I, J, K and Y, beta, confluent hypergeometric, error, gamma, log gamma, Pochhammer, Spence; integrals include hyperbolic cosine, cosine, Dawson, exponential, logarithmic, hyperbolic sine, sine; by Wayne Fullerton.

SPECFUN, a FORTRAN90 library which computes special functions, including Bessel I, J, K and Y functions, and the Dawson, E1, EI, Erf, Gamma, log Gamma, Psi/Digamma functions, by William Cody and Laura Stoltz;

SPECIAL_FUNCTIONS, a FORTRAN90 library which computes the Beta, Error, Gamma, Lambda, Psi functions, the Airy, Bessel I, J, K and Y, Hankel, Jacobian elliptic, Kelvin, Mathieu, Struve functions, spheroidal angular functions, parabolic cylinder functions, hypergeometric functions, the Bernoulli and Euler numbers, the Hermite, Laguerre and Legendre polynomials, the cosine, elliptic, exponential, Fresnel and sine integrals, by Shanjie Zhang, Jianming Jin;


  1. William Cody,
    Algorithm 715: SPECFUN - A Portable FORTRAN Package of Special Function Routines and Test Drivers,
    ACM Transactions on Mathematical Software,
    Volume 19, Number 1, March 1993, pages 22-32.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.

Last revised on 10 January 2016.