Gaurav Bhatnagar and Michael J. Schlosser

Elliptic well-poised Bailey transforms and lemmas on root systems

(51 pages)

Abstract. We list $A_n$, $C_n$ and $D_n$ extensions of the elliptic WP Bailey transform and lemma, given in the classical case 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. During our study, we discovered two new $A_n$ $_{12}V_{11}$ transformation formulas, that reduce to two new $A_n$ extension 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.

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