English

Short proofs of the elliptic beta integrals

Classical Analysis and ODEs 2011-02-15 v2

Abstract

We give elementary proofs of the univariate elliptic beta integral with bases q,p<1|q|, |p|<1 and its multiparameter generalizations to integrals on the AnA_n and CnC_n root systems. We prove also some new unit circle multiple elliptic beta integrals, which are well defined for q=1|q|=1, and their p0p\to 0 degenerations.

Keywords

Cite

@article{arxiv.math/0408369,
  title  = {Short proofs of the elliptic beta integrals},
  author = {V. P. Spiridonov},
  journal= {arXiv preprint arXiv:math/0408369},
  year   = {2011}
}

Comments

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

R2 v1 2026-07-22T17:09:08.608Z