Integrals Involving a Parameter

  • B. Davies
Part of the Applied Mathematical Sciences book series (AMS, volume 25)


Consider the function g(γ) defined by
$$ g(\gamma ) = 2{\pi ^{1/2}}{\gamma ^{3/2}}\int_0^\infty {\frac{{{e^{ - \gamma {k^2}}}}}{{{e^{\pi /k}} - 1}}kdk} $$


Asymptotic Expansion Integral Representation Asymptotic Form Simple Polis Asymptotic Series 
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  1. 1.
    B. Davies & R. G. Storer, Phys. Rev. (1968), 171, 150.CrossRefGoogle Scholar
  2. 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. 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. 4.
    Based on material written by B. W. Ninham.Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • B. Davies
    • 1
  1. 1.Department of MathematicsThe Australian National UniversityCanberraAustralia

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