gen_laguerre_rule, a MATLAB code 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 code 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 code which defines a nested Clenshaw Curtis quadrature rule.

chebyshev1_rule, a MATLAB code which can compute and print a Gauss-Chebyshev type 1 quadrature rule.

chebyshev2_rule, a MATLAB code which can compute and print a Gauss-Chebyshev type 2 quadrature rule.

clenshaw_curtis_rule, a MATLAB code which defines a Clenshaw Curtis quadrature rule.

gegenbauer_rule, a MATLAB code which can compute and print a Gauss-Gegenbauer quadrature rule.

gen_hermite_rule, a MATLAB code which computes a generalized Gauss-Hermite quadrature rule.


hermite_rule, a MATLAB code which computes a Gauss-Hermite quadrature rule.

jacobi_rule, a MATLAB code which computes a Gauss-Jacobi quadrature rule.

laguerre_rule, a MATLAB code which computes a Gauss-Laguerre quadrature rule.

legendre_rule, a MATLAB code which computes a Gauss-Legendre quadrature rule.

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

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

patterson_rule, a MATLAB code which computes a Gauss-Patterson quadrature rule.

power_rule, a MATLAB code 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 code which contains 1-dimensional quadrature rules.

truncated_normal_rule, a MATLAB code 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].


  1. Milton Abramowitz, Irene Stegun,
    Handbook of Mathematical Functions,
    National Bureau of Standards, 1964,
    ISBN: 0-486-61272-4,
    LC: QA47.A34.
  2. Philip Davis, Philip Rabinowitz,
    Methods of Numerical Integration,
    Second Edition,
    Dover, 2007,
    ISBN: 0486453391,
    LC: QA299.3.D28.
  3. Sylvan Elhay, Jaroslav Kautsky,
    Algorithm 655: IQPACK, FORTRAN Subroutines for the Weights of Interpolatory Quadrature,
    ACM Transactions on Mathematical Software,
    Volume 13, Number 4, December 1987, pages 399-415.
  4. Jaroslav Kautsky, Sylvan Elhay,
    Calculation of the Weights of Interpolatory Quadratures,
    Numerische Mathematik,
    Volume 40, 1982, pages 407-422.
  5. Roger Martin, James Wilkinson,
    The Implicit QL Algorithm,
    Numerische Mathematik,
    Volume 12, Number 5, December 1968, pages 377-383.
  6. Philip Rabinowitz, George Weiss,
    Tables of Abscissas and Weights for Numerical Evaluation of Integrals of the form $\int_0^{\infty} exp(-x) x^n f(x) dx$,
    Mathematical Tables and Other Aids to Computation,
    Volume 13, Number 68, October 1959, pages 285-294.
  7. Arthur Stroud, Don Secrest,
    Gaussian Quadrature Formulas,
    Prentice Hall, 1966,
    LC: QA299.4G3S7.

Source Code:

Last revised on 24 January 2019