Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems

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.