Limits of elliptic hypergeometric integrals

Details Limits of elliptic hypergeometric integrals Limits of elliptic hypergeometric integrals

2006-07-04

arxiv.org/abs/math/0607093v2

Mathematics

Classical Analysis and ODEs

41 pages LaTeX. Minor stylistic changes, statement of Theorem 4.7 fixed

Scientific paper

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.

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