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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. http://resolver.caltech.edu/CaltechAUTHORS:20090423-141245409

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s11139-007-9055-3DOIArticle
http://www.springerlink.com/content/h2827324863q50w3/PublisherArticle
http://rdcu.be/wce6PublisherFree ReadCube access
http://arxiv.org/abs/math/0607093arXivDiscussion Paper
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.
Funders:
Funding AgencyGrant Number
NSFDMS-0401387
Subject Keywords:elliptic gamma asymptotics; degeneration; hypergeometric integrals
Issue or Number:3
Record Number:CaltechAUTHORS:20090423-141245409
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20090423-141245409
Official Citation:Rains, E.M. Ramanujan J (2009) 18: 257. https://doi.org/10.1007/s11139-007-9055-3
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14057
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 Apr 2009 22:31
Last Modified:25 Sep 2017 22:42

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