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arXiv · 1901.01988

General Multi-sum Transformations and Some Implications

James Mc Laughlin
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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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James Mc Laughlin. 2019-01-06. General Multi-sum Transformations and Some Implications. https://doi.org/10.1007/s11139-015-9694-8

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