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 EulerGauss hypergeometric function and Selberg integral, as well as elliptic extensions of many other plain hypergeometric and $q$hypergeometric constructions. In particular, the Bailey chain technique, used for proving RogersRamanujan type identities, has been generalized to integrals. At the elliptic level it yields a solution of the YangBaxter equation as an integral operator with an elliptic hypergeometric kernel. We give a brief survey of the developments in this field.
 Publication:

arXiv eprints
 Pub Date:
 July 2013
 DOI:
 10.48550/arXiv.1307.2876
 arXiv:
 arXiv:1307.2876
 Bibcode:
 2013arXiv1307.2876S
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 15 pp., 1 fig., accepted in Proc. of the Conference "The Legacy of Srinivasa Ramanujan" (Delhi, India, December 2012)