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Mathematics of Computation

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Asymptotic expansions of multiple integrals of rapidly oscillating functions

Authors: T. Iwaniec and A. Lutoborski
Journal: Math. Comp. 50 (1988), 215-228
MSC: Primary 41A60
MathSciNet review: 917829
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Abstract: Expansions of multiple integrals

$\displaystyle \int_{{a_1}}^{{b_1}} \cdots \int_{{a_n}}^{{b_n}} {w({\sigma _1}{x_1}, \ldots ,{\sigma _n}{x_n})g({x_1}, \ldots ,{x_n})\;d{x_1} \cdots d{x_n},} $

where w is a function on $ {{\mathbf{R}}^n}$ which is $ ({b_k} - {a_k})$-periodic in the kth variable, $ k = 1, \ldots ,n$, and g is smooth, are given in terms of negative powers of the integers $ {\sigma _1}, \ldots ,{\sigma _n}$. Estimates of the remainder term in the expansion are also given.

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Article copyright: © Copyright 1988 American Mathematical Society

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