Limits of elliptic hypergeometric integrals

By E. Rains. 2006

69 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/215ff8130805db3d210737c59771b65e8e2cadc5

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

Elliptic Hypergeometry of Supersymmetric Dualities (2009, background): “Limits of the elliptic hypergeometric integrals (or of the elliptic hypergeometric series hidden behind them) matched with the elliptic curve degenerations brought to light new types of q-hypergeometric functions as well [66, 67] (see also [10]).”
The importance of the Selberg integral (2007, background): “The reduction of the elliptic Selberg integral (3.73) to the ordinary Selberg integral is rather cumbersome, requiring several limits, variables changes and specializations of parameters [ 126 ].”
Essays on the theory of elliptic hypergeometric functions (2008, methodology): “The representation (2.21) provides an alternative way for the reduction to this function (such a limiting transition was rigorously justiﬁed in a diﬀerent way in [18]). As follows from the results of [28], for a ﬁxed domain of values of parameters the function G(u;ω) converges in this limit to γ(u;ω”