An integral Representation of a 10ϕ9 and Continuous Bi-Orthogonal 10ϕ9 Rational Functions
- 1 June 1986
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 38 (3) , 605-618
- https://doi.org/10.4153/cjm-1986-030-6
Abstract
1. Introduction. One of the most remarkable q-extensions of the classical beta integral was recently introduced by Askey and Wilson [1] (1.1) where |q| < 1 and the pairwise products of {a, b, c, d} as a multiset do not belong to the set {qj, j = 0, – 1, – 2, …}. The contour C is the unit circle described in the positive direction, but with suitable deformations to separate the sequences of poles converging to zero from the sequences of poles diverging to infinity. The symbol (A; q)∞ is an infinite product defined by (1.2) whenever it converges.Keywords
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