Completeness of Coherent States Associated with Self-Similar Potentials and Ramanujan's Integral Extension of the Beta Function

Aspects of elliptic hypergeometric functions

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 brie…