Elliptic Hypergeometric Summations by Taylor Series Expansion and Interpolation

TL;DR

This paper develops new summation formulas for elliptic hypergeometric series using Taylor series and interpolation techniques, extending known results and connecting to cubic theta functions.

Contribution

It introduces novel elliptic hypergeometric summation identities by applying elliptic Taylor series expansions and interpolation methods, extending previous $q$-case results.

Findings

Derived new elliptic hypergeometric summation formulas

Extended well-poised elliptic case results

Connected identities with cubic theta functions

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.