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Factorization of Basic Hypergeometric Series (2507.04313v1)
Published 6 Jul 2025 in math.CO, math.CA, and math.QA
Abstract: The general problem of the factorization of a basic hypergeometric series is presented and discussed. The case of the general $_2\psi_2$ series is examined in detail. Connections are found with the theory of basic hypergeometric series on root systems. Alternative proofs of several well-known summation and transformation formulae, including Gustafson's generalization of Ramanujan's $_1\psi_1$ summation, are obtained incidentally.
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