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This article is cited in 3 scientific papers (total in 3 papers)
Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems
Gaurav Bhatnagar, Michael J. Schlosser Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
Abstract:
We list $A_n$, $C_n$ and $D_n$ extensions of the elliptic WP Bailey transform and lemma, given for $n=1$ by Andrews and Spiridonov. Our work requires multiple series extensions of Frenkel and Turaev's terminating, balanced and very-well-poised ${}_{10}V_9$ elliptic hypergeometric summation formula due to Rosengren, and Rosengren and Schlosser. In our study, we discover two new $A_n$ ${}_{12}V_{11}$ transformation formulas, that reduce to two new $A_n$ extensions of Bailey's $_{10}\phi_9$ transformation formulas when the nome $p$ is $0$, and two multiple series extensions of Frenkel and Turaev's sum.
Keywords:
$A_n$ elliptic and basic hypergeometric series; elliptic and basic hypergeometric series on root systems; well-poised Bailey transform and lemma.
Received: September 1, 2017; in final form March 13, 2018; Published online March 22, 2018
Citation:
Gaurav Bhatnagar, Michael J. Schlosser, “Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems”, SIGMA, 14 (2018), 025, 44 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1324 https://www.mathnet.ru/eng/sigma/v14/p25
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Abstract page: | 189 | Full-text PDF : | 98 | References: | 15 |
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