gen_laguerre_rule, a C++ 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 MIT license


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

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CHEBYSHEV2_RULE, a C++ code which can compute and print a Gauss-Chebyshev type 2 quadrature rule.

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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 C++ code which contains 1-dimensional quadrature rules.

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  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 10 March 2020.