Evans, Ronald J. Multidimensional beta and gamma integrals. (English) Zbl 0820.33001 Andrews, George E. (ed.) et al., The Rademacher legacy to mathematics. The centenary conference in honor of Hans Rademacher, July 21-25, 1992, Pennsylvania State University, University Park, PA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 166, 341-357 (1994). Author’s abstract: In 1980, Richard Askey conjectured several \(q\)- integral extensions of Selberg’s multidimensional beta integral formula. We prove the last (and most general) of these. The proof utilizes our multivariate extension of a \(q\)-integral of Andrews and Askey along with a \(q\)-extension of an innovative method of Greg Anderson. The remainder of the paper is devoted to an exposition of Anderson’s method as applied to Selberg’s gamma integrals. Bombieri proved the Mehta-Dyson gamma integral formula by taking a limiting case of Selberg’s beta integral formula, thus exploiting the extra parameters in the beta integral. Richard Askey stressed the importance of finding direct evaluations of such limiting cases without introduction of extra parameters. This can be accomplished via Anderson’s method, and we give detailed proofs.For the entire collection see [Zbl 0798.00010]. Reviewer: D.Kershaw (Lancaster) Cited in 2 ReviewsCited in 11 Documents MSC: 33B15 Gamma, beta and polygamma functions 33D05 \(q\)-gamma functions, \(q\)-beta functions and integrals Keywords:beta functions; gamma functions; gamma integrals; beta integral × Cite Format Result Cite Review PDF