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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Computation of integrals with oscillatory and singular integrands
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by Bing Yuan Ting and Yudell L. Luke PDF
Math. Comp. 37 (1981), 169-183 Request permission


This paper is concerned with evaluation of integrals whose integrands are oscillatory and contain singularities at the endpoints of the interval of integration. A typical form is $G(\theta ) = \smallint _a^bw(x){e^{i\theta x}}f(x) dx$, where a and b can be finite or infinite, $\theta$ is a parameter which is usually large, $f(x)$ is analytic in the range of integration, and the singularities are encompassed in the weight function $w(x)$. We suppose that $f(x)$ can be expanded in series of polynomials which are orthogonal over the interval of integration with respect to $w(x)$. There are two such expansions for $f(x)$. One is an infinite series which follows from the usual orthogonality property. The other is a polynomial approximation plus a remainder. The relations between the coefficients in these representations are detailed and methods for the evaluation of these are analyzed. Error analyses are provided. A numerical example is given to illustrate the effectiveness of the schemes developed.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 169-183
  • MSC: Primary 65D30; Secondary 41A60
  • DOI:
  • MathSciNet review: 616369