Elliptic WellPoised Bailey Transforms and Lemmas on Root Systems
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 verywellpoised ${}_{10}V_9$ 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.
 Publication:

SIGMA
 Pub Date:
 March 2018
 DOI:
 10.3842/SIGMA.2018.025
 arXiv:
 arXiv:1704.00020
 Bibcode:
 2018SIGMA..14..025B
 Keywords:

 An elliptic and basic hypergeometric series; elliptic and basic hypergeometric series on root systems; wellpoised Bailey transform and lemma;
 Mathematics  Classical Analysis and ODEs;
 33D67
 EPrint:
 SIGMA 14 (2018), 025, 44 pages