Aspects of elliptic hypergeometric functions
Abstract
General elliptic hypergeometric functions are defined by elliptic hypergeometric integrals. They comprise the elliptic beta integral, elliptic analogues of the Euler-Gauss hypergeometric function and Selberg integral, as well as elliptic extensions of many other plain hypergeometric and -hypergeometric constructions. In particular, the Bailey chain technique, used for proving Rogers-Ramanujan type identities, has been generalized to integrals. At the elliptic level it yields a solution of the Yang-Baxter equation as an integral operator with an elliptic hypergeometric kernel. We give a brief survey of the developments in this field.
Cite
@article{arxiv.1307.2876,
title = {Aspects of elliptic hypergeometric functions},
author = {V. P. Spiridonov},
journal= {arXiv preprint arXiv:1307.2876},
year = {2014}
}
Comments
15 pp., 1 fig., accepted in Proc. of the Conference "The Legacy of Srinivasa Ramanujan" (Delhi, India, December 2012)