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Inversion of bilateral basic hypergeometric series

Michael Schlosser
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Abstract

We present a new matrix inverse with applications in the theory of bilateral basic hypergeometric series. Our matrix inversion result is directly extracted from an instance of Bailey's very-well-poised 6-psi-6 summation theorem, and involves two infinite matrices which are not lower-triangular. We combine our bilateral matrix inverse with known basic hypergeometric summation theorems to derive, via inverse relations, several new identities for bilateral basic hypergeometric series.

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Michael Schlosser. 2002-06-05. Inversion of bilateral basic hypergeometric series. https://arxiv.org/abs/math/0206032

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