GEGENBAUER_CC
Gegenbauer Integral of a Function

GEGENBAUER_CC is a Python 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
      

Licensing:

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

Languages:

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

Related Data and Programs:

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

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.py, returns the even Chebyshev coefficients of F, using the extreme points of Tn(x).
• chebyshev_even2.py, returns the even Chebyshev coefficients of F, using the zeros of Tn(x).
• gegenbauer_cc1.py, estimates the Gegenbauer integral of a function.
• gegenbauer_cc2.py, estimates the Gegenbauer integral of a function.
• i4_uniform_ab.py, returns a scaled pseudorandom I4.
• r8_mop.py, returns the I-th power of -1 as an R8 value.
• r8vec_print.py, prints an R8VEC.
• r8vec2_print.py, prints a pair of R8VEC's.
• timestamp.py, prints the YMDHMS date as a timestamp.

Examples and Tests:

• gegenbauer_cc_test.py, calls all the tests;
• gegenbauer_cc_test.sh, runs all the tests;
• gegenbauer_cc_test.txt, the output file.

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