Gaurav Bhatnagar and Michael J. Schlosser

Elliptic well-poised Bailey transforms and lemmas on root systems

(44 pages)

Abstract. We list An, Cn and Dn 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 10V9 elliptic hypergeometric summation formula due to Rosengren, and Rosengren and Schlosser. In our study, we discover two new An 12V11 transformation formulas, that reduce to two new An extensions of Bailey's 10φ9 transformation formulas when the nome p is 0, and two multiple series extensions of Frenkel and Turaev's sum.

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