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On the numerical evaluation of some definite integrals

Published online by Cambridge University Press:  24 October 2008

W. Barrett
W. Barrett
Affiliation:
Department of Mathematics, The University, Leeds 2
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Abstract

An account is given of the application of Gaussian quadrature formulae to the numerical evaluation of certain definite integrals appearing in a recent paper by Craggs (2). Suitable changes of variable are used to effect a substantial reduction in the order of formula required. In comparing methods, use is made of an expression for the remainder as a contour integral, whose value is estimated with the aid of certain asymptotic formulae.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 1 , January 1964 , pp. 75 - 82
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1)Barrett, W.Convergence properties of Gaussian quadrature formulae. Comput. J. 3 (1960), 272–277CrossRefGoogle Scholar
(2)Craggs, J. W.On axially symmetric waves. III. Proc. Cambridge Philos. Soc. 59 (1963), 803–809CrossRefGoogle Scholar
(3)Szego, G.Orthogonal polynomials (American Math. Soc. Colloquium Publications, XXIII; New York, 1939).Google Scholar