Limits of elliptic hypergeometric integrals
经典分析与常微分方程
2007-09-05 v2
摘要
In math.QA/0309252, the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore more carefully the various limiting cases (hyperbolic, trigonometric, rational, and classical) that exist. In particular, we show (using some new estimates of generalized gamma functions) that the hyperbolic integrals (previously treated as purely formal limits) are indeed limiting cases. We also obtain a number of new trigonometric (q-hypergeometric) integral identities as limits from the elliptic level.
引用
@article{arxiv.math/0607093,
title = {Limits of elliptic hypergeometric integrals},
author = {Eric M. Rains},
journal= {arXiv preprint arXiv:math/0607093},
year = {2007}
}
备注
41 pages LaTeX. Minor stylistic changes, statement of Theorem 4.7 fixed