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General multi-sum transformations and some implications

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Abstract

We give two general transformations that allows certain quite general basic hypergeometric multi-sums of arbitrary depth (sums that involve an arbitrary sequence \(\{g(k)\}\)), to be reduced to an infinite q-product times a single basic hypergeometric sum. Various applications are given, including summation formulae for some q orthogonal polynomials and various multi-sums that are expressible as infinite products.

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Authors and Affiliations

  1. Mathematics Department, West Chester University, 25 University Avenue, West Chester, PA, 19383, USA

    James Mc Laughlin

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  1. James Mc Laughlin
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Correspondence to James Mc Laughlin.

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This work was partially supported by a Grant from the Simons Foundation (#209175 to James Mc Laughlin).

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Mc Laughlin, J. General multi-sum transformations and some implications. Ramanujan J 39, 545–565 (2016). https://doi.org/10.1007/s11139-015-9694-8

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  • DOI: https://doi.org/10.1007/s11139-015-9694-8

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