Uniformly asymptotic expansions for an integral with a large and a small parameter
1987 ◽
Vol 101
(2)
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pp. 349-362
Keyword(s):
AbstractThe integralinvolves a large real parameter N and a small real parameter ∈. Its asymptotic behaviour is non-uniform when N → ∞ and ∈ → 0. Thus, when ∈ > 0 is kept fixed and N → ∞, the integral decays exponentially at a rate depending on ∈; when ∈ → 0 the integral tends towhich decays algebraically when N → ∞. It is shown that several distinct uniformly asymptotic expansions can be obtained which each involve an infinite set of functions of the combination Certain related integrals are also treated.
2013 ◽
Vol 143
(6)
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pp. 1255-1289
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1980 ◽
Vol 87
(1)
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pp. 167-178
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1970 ◽
Vol 11
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pp. 84-84
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Vol 136
(6)
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pp. 1131-1155
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Vol 36
(5)
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pp. 924-960
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2020 ◽
Vol 150
(5)
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pp. 2682-2718
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2018 ◽
Vol 2018
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pp. 1-8