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A note on a generalized double series

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  • Robert Reynolds

Abstract

By employing contour integration the derivation of a generalized double finite series involving the Hurwitz-Lerch zeta function is used to derive closed form formulae in terms of special functions. We use this procedure to find special cases of the summation and product formulae in terms of the Hurwitz-Lerch zeta function, trigonometric functions and the gamma function. A short table of quotient gamma functions and plots are produced for easy reading by interested readers.

Suggested Citation

  • Robert Reynolds, 2026. "A note on a generalized double series," PLOS ONE, Public Library of Science, vol. 21(1), pages 1-24, January.
    • Handle: RePEc:plo:pone00:0340358
    DOI: 10.1371/journal.pone.0340358
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