Generalized Gauss-Laguerre Quadrature Rules

GEN_LAGUERRE_RULE, a MATLAB program which generates a specific generalized Gauss-Laguerre quadrature rule, based on user input.

The rule is written to three files for easy use as input to other programs.

The generalized Gauss-Laguerre quadrature rule is used as follows:

        Integral ( a <= x < +oo ) |x-a|^alpha * exp(-b*(x-a)) f(x) dx
is to be approximated by
        Sum ( 1 <= i <= order ) w(i) * f(x(i))


gen_laguerre_rule ( order, alpha, a, b, 'filename' )


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


GEN_LAGUERRE_RULE is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

ALPERT_RULE, a MATLAB library which can set up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.

CCN_RULE, a MATLAB program which defines a nested Clenshaw Curtis quadrature rule.

CHEBYSHEV1_RULE, a MATLAB program which can compute and print a Gauss-Chebyshev type 1 quadrature rule.

CHEBYSHEV2_RULE, a MATLAB program which can compute and print a Gauss-Chebyshev type 2 quadrature rule.

CLENSHAW_CURTIS_RULE, a MATLAB program which defines a Clenshaw Curtis quadrature rule.

GEGENBAUER_RULE, a MATLAB program which can compute and print a Gauss-Gegenbauer quadrature rule.

GEN_HERMITE_RULE, a MATLAB program which computes a generalized Gauss-Hermite quadrature rule.


HERMITE_RULE, a MATLAB program which computes a Gauss-Hermite quadrature rule.

INTLIB, a FORTRAN90 library which contains routines for numerical estimation of integrals in 1D.

JACOBI_RULE, a MATLAB program which computes a Gauss-Jacobi quadrature rule.

LAGUERRE_RULE, a MATLAB program which computes a Gauss-Laguerre quadrature rule.

LEGENDRE_RULE, a MATLAB program which computes a Gauss-Legendre quadrature rule.

LEGENDRE_RULE_FAST, a MATLAB program which uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature rule of given order.

LINE_FELIPPA_RULE, a MATLAB library which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.

PATTERSON_RULE, a MATLAB program which computes a Gauss-Patterson quadrature rule.

POWER_RULE, a MATLAB program which constructs a power rule, that is, a product quadrature rule from identical 1D factor rules.

QUADRATURE_RULES, a dataset directory which contains sets of files that define quadrature rules over various 1D intervals or multidimensional hypercubes.

QUADRATURE_RULES_LAGUERRE, a dataset directory which contains triples of files defining Gauss-Laguerre quadrature rules.

QUADRULE, a MATLAB library which contains 1-dimensional quadrature rules.

TEST_INT_LAGUERRE, a MATLAB library which defines test integrands for Gauss-Laguerre rules.

TRUNCATED_NORMAL_RULE, a MATLAB 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].


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    Handbook of Mathematical Functions,
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    Numerische Mathematik,
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    Mathematical Tables and Other Aids to Computation,
    Volume 13, Number 68, October 1959, pages 285-294.
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    Gaussian Quadrature Formulas,
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    LC: QA299.4G3S7.

Source Code:

Last revised on 24 January 2019