Elliptic Hypergeometric Summations by Taylor Series Expansion and Interpolation

Abstract

We use elliptic Taylor series expansions and interpolation to deduce a number of summations for elliptic hypergeometric series. We extend to the well-poised elliptic case results that in the $q$-case have previously been obtained by Cooper and by Ismail and Stanton. We also provide identities involving S. Bhargava's cubic theta functions.

Cited by in corpus (2)

• The noncommutative geometry of elliptic difference equations
• Further study on elliptic interpolation formulas for the elliptic Askey-Wilson polynomials and allied identities