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Limits of elliptic hypergeometric integrals

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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.

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Authors and Affiliations

  1. Department of Mathematics, California Institute of Technology, Mail Code 253-37, Pasadena, CA, 91125, USA

    Eric M. Rains

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  1. Eric M. Rains
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Correspondence to Eric M. Rains.

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The author was supported in part by NSF Grant No. DMS-0401387.

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Rains, E.M. Limits of elliptic hypergeometric integrals. Ramanujan J 18, 257–306 (2009). https://doi.org/10.1007/s11139-007-9055-3

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  • DOI: https://doi.org/10.1007/s11139-007-9055-3

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