Short proofs of the elliptic beta integrals

Details Short proofs of the elliptic beta integrals Short proofs of the elliptic beta integrals

2004-08-26

arxiv.org/abs/math/0408369v2

Ramanujan J. 13 (2007), 265-283

Mathematics

Classical Analysis and ODEs

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

Scientific paper

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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