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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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On a method of asymptotic evaluation of multiple integrals
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by R. Wong and J. P. McClure PDF
Math. Comp. 37 (1981), 509-521 Request permission


In this paper, some of the formal arguments given by Jones and Kline [J. Math. Phys., v. 37, 1958, pp. 1-28] are made rigorous. In particular, the reduction procedure of a multiple oscillatory integral to a one-dimensional Fourier transform is justified, and a Taylor-type theorem with remainder is proved for the Dirac $\delta$-function. The analyticity condition of Jones and Kline is now replaced by infinite differentiability. Connections with the asymptotic expansions of Jeanquartier and Malgrange are also discussed.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Math. Comp. 37 (1981), 509-521
  • MSC: Primary 41A60; Secondary 41A63
  • DOI:
  • MathSciNet review: 628712