Michael J. Schlosser, Meesue Yoo, “Elliptic Hypergeometric Summations by Taylor Series Expansion and Interpolation”, SIGMA, 2016, Volume 12,039, 21 pp.

This article is cited in 2 papers

Elliptic Hypergeometric Summations by Taylor Series Expansion and Interpolation

Michael J. Schlosser, Meesue Yoo

Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria

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.

Keywords: elliptic hypergeometric series; summations; Taylor series expansion; interpolation.

MSC: 30E05; 33D15; 33D70; 33E05; 33E20

Received: March 1, 2016; in final form April 13, 2016; Published online April 19, 2016

Language: English

DOI: 10.3842/SIGMA.2016.039