On an asymptotic expansion of Fourier integrals
1992 ◽
Vol 436
(1896)
◽
pp. 109-120
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Keyword(s):
A formula is developed that gives the asymptotic expansion of the Fourier transform of a function whose behaviour near the origin is given by a general asymptotic series. The result is an extension of a theorem due to Olver, who obtained a kind of analogue for Fourier transforms of Watson’s lemma for Laplace transforms. The method adopted utilizes a result due to Erdelyi on Laplace transforms and depends for its success on a novel technique of evading the appearance of divergent integrals in such problems.
1986 ◽
Vol 38
(2)
◽
pp. 328-359
◽
1965 ◽
Vol 61
(3)
◽
pp. 617-620
◽
1991 ◽
Vol 33
(2)
◽
pp. 180-191
◽
2003 ◽
Vol 133
(4)
◽
pp. 943-950
◽
1990 ◽
Vol 13
(3)
◽
pp. 431-441