Summation, transformation, and expansion formulas for multibasic theta hypergeometric series
Classical Analysis and ODEs
2007-05-23 v1
Abstract
After reviewing some fundamental facts from the theory of theta hypergeometric series we derive, using indefinite summation, several summation, transformation, and expansion formulas for multibasic theta hypergeometric series. Some of the identities presented here generalize corresponding formulas given in Chapter 11 of the Gasper and Rahman book [Basic hypergeometric series, 2nd ed., Encyclopedia of Mathematics And Its Applications 96, Cambridge University Press, Cambridge, 2004].
Cite
@article{arxiv.math/0505215,
title = {Summation, transformation, and expansion formulas for multibasic theta hypergeometric series},
author = {George Gasper and Michael Schlosser},
journal= {arXiv preprint arXiv:math/0505215},
year = {2007}
}
Comments
18 pages; for the proceedings of the workshop "Elliptic Integrable Systems" (RIMS, Kyoto, November 8-11, 2004), special volume of the Rokko Lectures in Mathematics