General multi-sum transformations and some implications |
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Authors: | James Mc Laughlin |
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Institution: | 1.Mathematics Department,West Chester University,West Chester,USA |
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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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