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Continuous q-Hermite polynomials when q>1. (English) Zbl 0694.33006
q-Series and partitions, Proc. Workshop, Minneapolis/MN (USA) 1988, IMA Vol. Math. Appl. 18, 151-158 (1989).

[For the entire collection see Zbl 0687.00005.]

If xix in the recurrence relation for the continuous q-Hermite polynomials of Rogers, the resulting polynomials are orthogonal on the real line with respect to a positive measure when q>1. Some explicit orthogonality relations are given here. The moment problem is indeterminate so there are many positive measures which can be used. One of these orthogonalities led to a new q-beta integral with four free parameters.

Reviewer: R.Askey

33C45Orthogonal polynomials and functions of hypergeometric type