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

Canadian Journal of Mathematics - Tập 38 Số 3 - Trang 605-618 - 1986
Mizan Rahman1
1Carleton University, Ottawa, Ontario

Tóm tắt

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.

Từ khóa


Tài liệu tham khảo

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Bailey, 1947, Quart. J. Math. (Oxford), Well-poised basic hyper geometric series, 18, 157

Askey, 1985, Mem. Amer. Math. Soc., Some basic hyper geometric polynomials that generalize Jacobi polynomials, 54

Wilson J. A. private communication.

Nassrallah, 1985, SIAM J. Math. Anal., Projection formulas, a reproducing kernel and a generating function for q-Wilson polynomials, 16, 186

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Thông tin xuất bản

Canadian Journal of Mathematics

Tập 38 Số 3

605-618

Thông tin tác giả