The Ramanujan Journal

, Volume 13, Issue 1–3, pp 265–283

Short proofs of the elliptic beta integrals


DOI: 10.1007/s11139-006-0252-2

Cite this article as:
Spiridonov, V.P. Ramanujan J (2007) 13: 265. doi:10.1007/s11139-006-0252-2


We give elementary proofs of the univariate elliptic beta integral with bases |q|,|p| < 1 and its multiparameter generalizations to integrals on the An and Cn root systems. We prove also some new unit circle multiple elliptic beta integrals, which are well defined for |q| = 1, and their p → 0 degenerations.


Beta integrals Elliptic hypergeometric functions 

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Bogoliubov Laboratory of Theoretical PhysicsJINR, DubnaMoscowRussia

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