Expansion formulas for elliptic hypergeometric series

2024/03/06 by Gaurav Bhatnagar, Bhatnagar, Gaurav, Archna Kumari +1
Computer Science · Mathematics · #33E20 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Polynomial and algebraic computation #Primary 33D15 #Secondary 33D65

paper · pdf · doi:10.48550/arxiv.2403.03623

openalex publication_date 2024/03/06 · openalex created_date 2024/03/08 · openalex updated_date 2026/07/28

Abstract

We provide an alternate approach to obtaining expansion formulas on the lines of the well-poised Bailey lemma. We recover results due to Spiridonov and Warnaar and one new formula of this type. These formulas contain an arbitrary sequence as an argument, and are thus flexible in the number of parameters they contain. As a result, we are able to derive 19 new transformation formulas for elliptic hypergeometric series. These transformation formulas appear to be new even in the basic hypergeometric case, when p=0.

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