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Hyperbolic beta integrals | | Jasper V. Stokman
; | | Date: |
14 Mar 2003 | | Subject: | Quantum Algebra; Classical Analysis and ODEs | math.QA math.CA | | 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 $(q,widetilde{q})$-bibasic analogues of the beta integral in which the two bases $q$ and $widetilde{q}$ 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. | | Source: | arXiv, math.QA/0303178 | | Services: | Forum | Review | PDF | Favorites | |
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