fn, an Octave code which approximates elementary and special functions using Chebyshev polynomials; functions include Airy, Bessel I, Bessel J, Bessel K, Bessel Y, beta, confluent hypergeometric, cosine integral, Dawson's integral, digamma (psi), error, exponential integral, gamma, hyperbolic cosine integral, hyperbolic sine integral, incomplete gamma, log gamma, logarithmic integral, Pochhammer, psi, sine integral, Spence; by Wayne Fullerton.

The original version of the library provided routines for single precision complex, single precision real, and double precision real arguments and used the prefixes "C" and "D" to indicate the complex and double precision versions.

This scheme has been modified for consistency, and also to avoid conflict with the names of functions commonly provided by various compilers. The prefixes "C4_", and "R8_" are used to indicate functions for single precision complex, and double precision real arguments. For example, the sine function can be calculated by the functions C4_SIN or R8_SIN.

The original, true, correct version of FN is available through NETLIB: https://www.netlib.org/fn/index.html.


The computer code and data files described and made available on this web page are distributed under the MIT license


fn is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

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machine, an Octave code which stores the appropriate values of machine constants for a given machine.

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  1. Wayne Fullerton,
    Portable Special Function Routines,
    in Portability of Numerical Software,
    edited by Wayne Cowell,
    Lecture Notes in Computer Science, Volume 57, pages 452-483,
    Springer 1977,
    ISBN: 978-3-540-08446-4,
    LC: QA297.W65.

Source Code:

Last revised on 18 January 2019.