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Integrals Involving a Parameter

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Integral Transforms and their Applications

Part of the book series: Applied Mathematical Sciences ((AMS,volume 25))

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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)

.

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Footnotes

  1. B. Davies & R. G. Storer, Phys. Rev. (1968), 171, 150.

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  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).

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  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.

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  4. Based on material written by B. W. Ninham.

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Authors and Affiliations

  1. Department of Mathematics, The Australian National University, Post Office Box 4, Canberra, A.C.T., 2600, Australia

    B. Davies

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  1. B. Davies
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© 1985 Springer Science+Business Media New York

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Davies, B. (1985). Integrals Involving a Parameter. In: Integral Transforms and their Applications. Applied Mathematical Sciences, vol 25. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-2691-3_14

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  • DOI: https://doi.org/10.1007/978-1-4899-2691-3_14

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96080-7

  • Online ISBN: 978-1-4899-2691-3

  • eBook Packages: Springer Book Archive

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