Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 039, 21 pages      arXiv:1602.09027      https://doi.org/10.3842/SIGMA.2016.039
Contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications

Elliptic Hypergeometric Summations by Taylor Series Expansion and Interpolation

Michael J. Schlosser and Meesue Yoo
Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria

Received March 01, 2016, in final form April 13, 2016; Published online April 19, 2016

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.

Key words: elliptic hypergeometric series; summations; Taylor series expansion; interpolation.

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