Integral Transforms and their Applications pp 225-236 | Cite as
Integrals Involving a Parameter
Chapter
Abstract
Consider the function g(γ) defined by
.
$$ g(\gamma ) = 2{\pi ^{1/2}}{\gamma ^{3/2}}\int_0^\infty {\frac{{{e^{ - \gamma {k^2}}}}}{{{e^{\pi /k}} - 1}}kdk} $$
(1)
Keywords
Asymptotic Expansion Integral Representation Asymptotic Form Simple Polis Asymptotic Series
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Footnotes
- 1.B. Davies & R. G. Storer, Phys. Rev. (1968), 171, 150.CrossRefGoogle Scholar
- 2.A comprehensive analysis of the use of Mellin transforms to investigate integrals of the form (4) may be found in Bleistein and Handelsman (1975).Google Scholar
- 3.These results were obtained by H. C. Levey and J. J. Mahony, Q. Appl. Math. (1967), 26, 101, by a direct analysis. It is interesting to compare the two methods of derivation.MathSciNetGoogle Scholar
- 4.Based on material written by B. W. Ninham.Google Scholar
Copyright information
© Springer Science+Business Media New York 1985