# GEGENBAUER_CC 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.

### Languages:

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.

### 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.

### List of Routines:

• BESSELJ evaluates the Bessel J function at an arbitrary real order.
• CHEBYSHEV_EVEN1 returns the even Chebyshev coefficients of F.
• CHEBYSHEV_EVEN2 returns the even Chebyshev coefficients of F.
• GEGENBAUER_CC1 estimates the Gegenbauer integral of a function.
• GEGENBAUER_CC2 estimates the Gegenbauer integral of a function.
• I4_UNIFORM_AB returns a scaled pseudorandom I4 between A and B.
• R8_MOP returns the I-th power of -1 as an R8.
• R8VEC_PRINT prints an R8VEC.
• R8VEC2_PRINT prints an R8VEC2.
• RJBESL evaluates a sequence of Bessel J functions.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.

Last revised on 10 January 2016.