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Some curious q-series expansions and beta integral evaluations

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Abstract

We deduce several curious q-series expansions by applying inverse relations to certain identities for basic hypergeometric series. After rewriting some of these expansions in terms of q-integrals, we obtain, in the limit q→ 1, some curious beta-type integral evaluations which appear to be new.

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Authors and Affiliations

  1. Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois, 60208-2730

    George Gasper

  2. Institut für Mathematik der Universität Wien, Nordbergstraße 15, A-1090, Wien, Austria

    Michael Schlosser

Authors
  1. George Gasper
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  2. Michael Schlosser
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Corresponding author

Correspondence to George Gasper.

Additional information

Dedicated to Dick Askey on the occasion of his 70th birthday.

2000 Mathematics Subject Classification Primary—15A09, 33D15, 33E20; Secondary—05A30

M. Schlosser was fully supported by an APART fellowship of the Austrian Academy of Sciences.

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Gasper, G., Schlosser, M. Some curious q-series expansions and beta integral evaluations. Ramanujan J 13, 227–240 (2007). https://doi.org/10.1007/s11139-006-0249-x

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  • DOI: https://doi.org/10.1007/s11139-006-0249-x

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