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An integral Representation of a 10ϕ9 and Continuous Bi-Orthogonal 10ϕ9 Rational Functions

Published online by Cambridge University Press:  20 November 2018

Mizan Rahman
Mizan Rahman*
Affiliation:
Carleton University, Ottawa, Ontario
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 3 , 01 June 1986 , pp. 605 - 618
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Askey, R. and Wilson, J. A., Some basic hyper geometric polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54 (1985).Google Scholar
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5. Slater, L. J., Generalized hyper geometric functions (Cambridge University Press, 1966).Google Scholar
6. Wilson, J. A., Some hyper geometric orthogonal polynomials, SIAM J. Math. 11 (1980), 690–701.Google Scholar
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