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arXiv · 1602.00316

On Certain Generalizations of Rogers-Ramanujan Type Identities

Ahmad El-Guindy·Mourad E. H. Ismail
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Abstract

We state and prove a number of unilateral and bilateral $q$-series identities and explore some of their consequences. Those include certain generalizations of the $q$-binomial sum which also generalize the $q$-Airy function introduced by Ramanujan, as well as certain identities with an interesting variable-parameter symmetry based on limiting cases of Heine's transformation of basic hypergeomteric functions.

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Ahmad El-Guindy, Mourad E. H. Ismail. 2016-01-31. On Certain Generalizations of Rogers-Ramanujan Type Identities. https://arxiv.org/abs/1602.00316

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