, Volume 31, Issue 1-2, pp 213-238
Date: 25 Sep 2012

Variants of classical q-hypergeometric identities and partition implications

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Abstract

Utilizing a six-variable extension of Heine’s q-hypergeometric transformation that we previously obtained, we now derive variants of Heine’s transformation formula and the Lebesgue identity. The variant of Cauchy’s identity also obtained by us earlier is crucial in these derivations. We then establish some new partition identities which are variants of, and shed new light on, some fundamental classical partition identities.

Dedicated to Mourad Ismail and Dennis Stanton
Research supported in part by NSA Grants MSPF-06G-150 and MSPF-08G-154.