Hyperbolic beta integrals

Jasper V Stokman

doi:10.1016/j.aim.2003.12.003

Jasper V Stokman

Open Access

https://doi.org/10.1016/j.aim.2003.12.003

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Journal: Advances in Mathematics	Publication Date: Mar 18, 2004
Citations: 43	License type: elsevier-specific: oa user license

Affiliation: Vrije Universiteit Amsterdam, University of Amsterdam

Abstract

Hyperbolic beta integrals are analogues of Euler's beta integral in which the role of Euler's gamma function is taken over by Ruijsenaars’ hyperbolic gamma function. They may be viewed as (q, q ̃ ) -bibasic analogues of the beta integral in which the two bases q and q̃ are interrelated by modular inversion, and they entail q-analogues of the beta integral for | q|=1. The integrals under consideration are the hyperbolic analogues of the Ramanujan integral, the Askey–Wilson integral and the Nassrallah–Rahman integral. We show that the hyperbolic Nassrallah–Rahman integral is a formal limit case of Spiridonov's elliptic Nassrallah–Rahman integral.

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