Evaluation of Special Functions

SPECIAL_FUNCTIONS is a FORTRAN77 library which computes the value of various special functions, by Shanjie Zhang, Jianming Jin.

The library includes functions for the Beta, Error, Gamma, Lambda, Psi functions, for the Airy, Bessel I, J, K and Y, Hankel, Jacobian elliptic, Kelvin, Mathieu, Struve functions, for spheroidal angular functions, parabolic cylinder functions, hypergeometric functions, for the Bernoulli and Euler numbers, for the Hermite, Laguerre and Legendre polynomials, for the cosine, elliptic, exponential, Fresnel and sine integrals.

Jianming Jin makes the text of the original FORTRAN77 source code available at http://in.ece.illinois.edu/routines/routines.html.


The FORTRAN77 source code of this library is copyrighted by Shanjie Zhang and Jianming Jin. However, they give permission to incorporate routines from this library into a user program provided that the copyright is acknowledged.


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

Related Data and Programs:

CORDIC, a FORTRAN77 library which uses the CORDIC method to compute certain elementary functions.

FN, a FORTRAN77 library which evaluates elementary and special functions, by Wayne Fullerton.

POLPAK, a FORTRAN77 library which evaluates certain mathematical functions, especially some recursive polynomial families.

SLATEC, a FORTRAN90 library which evaluates many special functions.

SPECFUN, a FORTRAN77 library which computes special functions, including Bessel I, J, K and Y functions, and the Dawson, E1, EI, Erf, Gamma, Psi/Digamma functions, by William Cody and Laura Stoltz;

TEST_VALUES, a FORTRAN77 library which contains a few test values of many functions.

TOMS644, a FORTRAN77 library which evaluates the Bessel I, J, K, Y functions, the Airy functions Ai and Bi, and the Hankel function, for complex argument and real order.

TOMS715, a FORTRAN77 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.


  1. Shanjie Zhang, Jianming Jin,
    Computation of Special Functions,
    Wiley, 1996,
    ISBN: 0-471-11963-6,
    LC: QA351.C45.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN77 source codes.

Last revised on 12 April 2012.