Short proofs of the elliptic beta integrals

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.

15 pages; minor textual corrections, to appear in Ramanujan J

References in corpus (2)

• The elliptic gamma function and SL(3,Z) x Z^3
• Transformations of elliptic hypergometric integrals

Cited by in corpus (4)

• Properties of generalized univariate hypergeometric functions
• Transformations of elliptic hypergometric integrals
• A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities
• Inversions of integral operators and elliptic beta integrals on root systems