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General Multi-sum Transformations and Some Implications (1901.01988v1)
Published 6 Jan 2019 in math.NT
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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