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.
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_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:
-
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:
-
BESSELJ evaluates the Bessel J function at an arbitrary real order.
-
CHEBYSHEV_EVEN1 returns the even Chebyshev coefficients of F.
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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.
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I4_UNIFORM_AB returns a scaled pseudorandom I4 between A and B.
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R8_MOP returns the I-th power of -1 as an R8.
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R8VEC_PRINT prints an R8VEC.
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R8VEC2_PRINT prints an R8VEC2.
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RJBESL evaluates a sequence of Bessel J functions.
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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.