, Volume 13, Issue 1-3, pp 265-283

Short proofs of the elliptic beta integrals

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Abstract

We give elementary proofs of the univariate elliptic beta integral with bases |q|,|p| < 1 and its multiparameter generalizations to integrals on the A n and C n 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.

Dedicated to Richard Askey on the occasion of his seventieth birthday.
2000 Mathematics Subject Classification Primary—33D99, 33E05
This work is supported in part by the Russian Foundation for Basic Research (RFBR) grant no. 03-01-00781.