gegenbauer_cc, an Octave code 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 MIT license


gegenbauer_cc 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.

Related Data and Programs:


gegenbauer_exactness, an Octave code which tests the monomial exactness of Gauss-Gegenbauer quadrature rules.

gegenbauer_polynomial, an Octave code which evaluates the Gegenbauer polynomial and associated functions.

gegenbauer_rule, an Octave code which computes and prints 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:

Last modified on 23 January 2019.