chebyshev2_rule, an Octave code which generates a specific Gauss-Chebyshev type 2 quadrature rule, based on user input.

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

The Gauss-Chevbyshev type 2 quadrature rule is used as follows:

        Integral ( A <= x <= B ) f(x)  sqrt ( ( x - A ) * ( B - x ) ) dx
is to be approximated by
        Sum ( 1 <= i <= order ) w(i) * f(x(i))


chebyshev2_rule ( order, a, b, 'filename' )


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


chebyshev2_rule is available in a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and Programs:


alpert_rule, an Octave code which can set up an alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.

ccn_rule, an Octave code which defines a nested clenshaw curtis quadrature rule.

chebyshev_polynomial, an Octave code which evaluates the chebyshev polynomial and associated functions.

chebyshev1_rule, an Octave code which can compute and print a gauss-chebyshev type 1 quadrature rule.

clenshaw_curtis_rule, an Octave code which defines a clenshaw curtis quadrature rule.

gegenbauer_rule, an Octave code which can compute and print a gauss-gegenbauer quadrature rule.

gen_hermite_rule, an Octave code which can compute and print a generalized gauss-hermite quadrature rule.

gen_laguerre_rule, an Octave code which can compute and print a generalized gauss-laguerre quadrature rule.

hermite_rule, an Octave code which can compute and print a gauss-hermite quadrature rule.

jacobi_rule, an Octave code which can compute and print a gauss-jacobi quadrature rule.

laguerre_rule, an Octave code which can compute and print a gauss-laguerre quadrature rule.

legendre_rule, an Octave code which can compute and print a gauss-legendre quadrature rule.

line_felippa_rule, an Octave code which returns the points and weights of a felippa quadrature rule over the interior of a line segment in 1d.

patterson_rule, an Octave code which computes a gauss-patterson quadrature rule.

power_rule, an Octave code which constructs a power rule, that is, a product quadrature rule from identical 1d factor rules.

quadrature_rules_chebyshev2, a dataset directory which contains triples of files defining standard gauss-chebyshev type 2 quadrature rules.

quadrule, an Octave code which defines 1-dimensional quadrature rules.

truncated_normal_rule, an Octave 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. Arthur Stroud, Don Secrest,
    Gaussian Quadrature Formulas,
    Prentice Hall, 1966,
    LC: QA299.4G3S7.

Source Code:

Last revised on 10 December 2018.