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Limits of elliptic hypergeometric integrals

Rains, Eric M. (2009) Limits of elliptic hypergeometric integrals. Ramanujan Journal, 18 (3). pp. 257-306. ISSN 1382-4090.

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In Ann. Math., to appear, 2008, 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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Additional Information:© 2009 Springer. Received: 14 April 2007. Accepted: 20 August 2007. Published online: 31 October 2007. The author would like to thank P. Forrester, J. Stokman and F. van de Bult for motivating conversations regarding the trigonometric and hyperbolic cases, and R. Askey for suggesting the use of the modular transformation to derive classical limits (as in [10]), which led the author to consider the paper [9]; the author would also like to thank an anonymous referee for pointing out that the original version of Theorem 4.7 was badly stated.
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Subject Keywords:elliptic gamma asymptotics; degeneration; hypergeometric integrals
Issue or Number:3
Record Number:CaltechAUTHORS:20090423-141245409
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Official Citation:Rains, E.M. Ramanujan J (2009) 18: 257.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14057
Deposited By: Tony Diaz
Deposited On:24 Apr 2009 22:31
Last Modified:03 Oct 2019 00:46

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