English

Aspects of elliptic hypergeometric functions

Classical Analysis and ODEs 2014-07-01 v1 High Energy Physics - Theory Mathematical Physics math.MP

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 qq-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.

Keywords

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)

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