## 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

## Abstract:

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: https://doi.org/10.1090/S0025-5718-1981-0628712-1
- MathSciNet review: 628712