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Mellin Transforms in Summation

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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

Suppose we wish to evaluate the sum

$$ S = \sum\limits_{n = 1}^\infty {f(n)} $$
(1)

.

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Footnotes

  1. This section is based on G. G. MacFarlane, Phil. Mag. (vii) (1949), 40, 188. MacFarlane considers the more general problem of evaluating sums of the form

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  2. This treatment is due to B. W. Nini. am.

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  3. Dingle (1973), Ch. 2.

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  4. For example, Olver (1974), p. 64.

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  5. This is a transformation in the theory of elliptic modular functions.

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Author information

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). Mellin Transforms in Summation. 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_13

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  • DOI: https://doi.org/10.1007/978-1-4899-2691-3_13

  • 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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