Orthogonality relations for Al-Salam--Carlitz polynomials of type II

Abstract

Using a special case of Askey's $q$-beta integral evaluation formula, we determine orthogonality relations for the Al-Salam--Carlitz polynomials of type II with respect to a family of measures supported on a discrete subset of $\mathbb{R}$. From spectral analysis of the corresponding second-order $q$-difference operator we obtain an infinite set of functions that complement the Al-Salam--Carlitz II polynomials to an orthogonal basis of the associated $L^2$-space.

15 pages

References in corpus (2)

• The indeterminate moment problem for the $q$-Meixner polynomials
• Coupling coefficients for tensor product representations of quantum $\mathrm{SU}(2)$

Cited by in corpus (2)

• Coupling coefficients for tensor product representations of quantum $\mathrm{SU}(2)$
• A solution to the Al-Salam--Chihara moment problem