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Short proofs of the elliptic beta integrals

V. P. Spiridonov
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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 $p\to 0$ degenerations.

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V. P. Spiridonov. 2004-08-26. Short proofs of the elliptic beta integrals. https://arxiv.org/abs/math/0408369

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