GEGENBAUER_RULE is a C++ program which generates a specific Gauss-Gegenbauer quadrature rule, based on user input.
The rule is written to three files for easy use as input to other programs.
The Gauss-Gegenbauer quadrature rule is used as follows:
Integral ( A <= x <= B ) ((x-A)(B-X))^alpha f(x) dxis to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))where alpha is a real parameter greater than -1.
gegenbauer_rule order alpha a b filenamewhere
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
GEGENBAUER_RULE is available in a C++ version and a FORTRAN90 version and a MATLAB version.
CCN_RULE, a C++ program which defines a nested Clenshaw Curtis quadrature rule.
CHEBYSHEV1_RULE, a C++ program which can compute and print a Gauss-Chebyshev type 1 quadrature rule.
CHEBYSHEV2_RULE, a C++ program which can compute and print a Gauss-Chebyshev type 2 quadrature rule.
CLENSHAW_CURTIS_RULE, a C++ program which defines a Clenshaw Curtis quadrature rule.
GEN_HERMITE_RULE, a C++ program which can compute and print a generalized Gauss-Hermite quadrature rule.
GEN_LAGUERRE_RULE, a C++ program which can compute and print a generalized Gauss-Laguerre quadrature rule.
HERMITE_RULE, a C++ program which can compute and print a Gauss-Hermite quadrature rule.
INT_EXACTNESS, a C++ program which checks the polynomial exactness of a 1-dimensional quadrature rule for a finite interval.
INT_EXACTNESS_JACOBI, a C++ program which checks the polynomial exactness of a Gauss-Jacobi rule.
INTLIB, a FORTRAN90 library which contains routines for numerical estimation of integrals in 1D.
JACOBI_RULE, a C++ program which can compute and print a Gauss-Jacobi quadrature rule.
LAGUERRE_RULE, a C++ program which can compute and print a Gauss-Laguerre quadrature rule.
LEGENDRE_RULE, a C++ program which computes a Gauss-Legendre quadrature rule.
LINE_FELIPPA_RULE, a C++ library which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.
LINE_NCO_RULE, a C++ library which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
PATTERSON_RULE, a C++ program which computes a Gauss-Patterson quadrature rule.
QUADRATURE_RULES, a dataset directory which contains sets of files that define quadrature rules over various 1D intervals or multidimensional hypercubes.
QUADRATURE_RULES_GEGENBAUER, a dataset directory which contains triples of files defining Gauss-Gegenbauer quadrature rules.
QUADRULE, a C++ library which contains 1-dimensional quadrature rules.
TANH_SINH_RULE, a C++ program which computes and writes out a tanh-sinh quadrature rule of given order.
TRUNCATED_NORMAL_RULE, a C++ program which computes a quadrature rule for a normal probability density function (PDF), also called a Gaussian distribution, that has been truncated to [A,+oo), (-oo,B] or [A,B].
gegenbauer_rule 4 2.0 -1.0 +1.0 gegen_o4_a2.0
gegenbauer_rule 4 2.0 -1.0 +1.0 gegen_o4_a2.0
gegenbauer_rule 4 2.0 -1.0 +1.0 gegen_o4_a2.0
You can go up one level to the C++ source codes.