Askey, Richard 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 \(x\to ix\) 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 Cited in 2 ReviewsCited in 19 Documents MSC: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) Keywords:q-Hermite polynomials; q-Hermite polynomials of Rogers Citations:Zbl 0687.00005 PDFBibTeX XML Digital Library of Mathematical Functions: §18.28(vii) Continuous 𝑞⁻¹-Hermite Polynomials ‣ §18.28 Askey–Wilson Class ‣ Other Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials