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 $q$-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.
- Pub Date:
- July 2013
- Mathematics - Classical Analysis and ODEs;
- High Energy Physics - Theory;
- Mathematical Physics
- 15 pp., 1 fig., accepted in Proc. of the Conference "The Legacy of Srinivasa Ramanujan" (Delhi, India, December 2012)