gegenbauer_cc

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
      

Licensing:

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

Languages:

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_cc_test

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.

Reference:

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:

• chebyshev_even1.m, returns the even Chebyshev coefficients of F, using the extreme points of Tn(x).
• chebyshev_even2.m, returns the even Chebyshev coefficients of F, using the zeros of Tn(x).
• gegenbauer_cc1.m, estimates the Gegenbauer integral of a function.
• gegenbauer_cc2.m, estimates the Gegenbauer integral of a function.
• r8_mop.m, returns the I-th power of -1 as an R8 value.
• r8vec_print.m, prints an R8VEC.
• r8vec2_print.m, prints a pair of R8VEC's.