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

Journal Article (2015)
Author(s)

Wolter Groenevelt (TU Delft - Analysis)

Research Group
Analysis
DOI related publication
https://doi.org/10.1016/j.jat.2014.07.006
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Publication Year
2015
Language
English
Research Group
Analysis
Volume number
195
Pages (from-to)
89-108

Abstract

By use of a special case of Slater’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 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 L2-space.

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