Gegenbauer Integral of a Function

GEGENBAUER_CC is a FORTRAN90 library which uses a Clenshaw-Curtis approach to approximate the integral of a function f(x) with a Gegenbauer weight.

The Gegenbauer integral of a function f(x) is:

        value = integral ( -1 <= x <= + 1 ) ( 1 - x^2 )^(lambda-1/2) * f(x) dx
where -0.5 < lambda.


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


GEGENBAUER_CC is available in a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

GEGENBAUER_EXACTNESS, a FORTRAN90 program which tests the monomial exactness of Gauss-Gegenbauer quadrature rules.

GEGENBAUER_POLYNOMIAL, a FORTRAN90 library which evaluates the Gegenbauer polynomial and associated functions.

GEGENBAUER_RULE, a FORTRAN90 program which can compute and print a Gauss-Gegenbauer quadrature rule.


  1. D B Hunter, H V Smith,
    A quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight function,
    Journal of Computational and Applied Mathematics,
    Volume 177, 2005, pages 389-400.

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.