Published April 2009
| Submitted
Journal Article
Open
Limits of elliptic hypergeometric integrals
- Creators
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Rains, Eric M.
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.
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.Attached Files
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Additional details
- Eprint ID
- 14057
- Resolver ID
- CaltechAUTHORS:20090423-141245409
- DMS-0401387
- NSF
- Created
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2009-04-24Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field