Abstract
By applying the theory of completely symmetric functions we derive a Gaussian quadrature rule which generalizes that due to McNamee. A feature of this generalization is the inclusion of an explicit correction term taking account of the presence of poles (of any order) of the integrand close to the integration-interval. A numerical example is provided to illustrate the formulae.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D.B. Hunter,Some Gauss-type formulae for the evaluation of Cauchy-principal values of integrals, Numer. Math., 19, 1972, 419–424.
D. E. Littlewood,A University Algebra, 2nd ed., Heinemann, London, 1958.
F. G. Lether,Subtracting out complex singularities in numerical integration, Math. Comp., 31, 1977, 223–229.
F. E. Lether,Modified quadrature formulas for functions with nearby poles. J. Comp. and Appl. Math., 3, 1977, 3–9.
J. McNamee,Error-bounds for the evaluation of integrals by the Euler-Maclaurin formula and by Gauss-type formulae, Math. Comp., 18, 1964, 368–381.
J. C. P. Miller, British Association for the Advancement of Science,Mathematical Tables, Volume X, Bessel Functions, Part II, Functions of Positive Integer Order, Camb. Univ. Press, 1952.
G. E. Okecha,Numerical Quadrature Involving Singular and Non-singular Integrals, Ph.D. Thesis, University of Bradford, 1985.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hunter, D.B., Okecha, G.E. A modified Gaussian quadrature rule for integrals involving poles of any order. BIT 26, 233–240 (1986). https://doi.org/10.1007/BF01933749
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01933749