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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