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arXiv · 0911.0205

The indeterminate moment problem for the $q$-Meixner polynomials

Wolter Groenevelt·Erik Koelink
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Abstract

For a class of orthogonal polynomials related to the $q$-Meixner polynomials corresponding to an indeterminate moment problem we give a one-parameter family of orthogonality measures. For these measures we complement the orthogonal polynomials to an orthogonal basis for the corresponding weighted $L^2$-space explicitly. The result is proved in two ways; by a spectral decomposition of a suitable operator and by direct series manipulation. We discuss extensions to explicit non-positive measures and the relation to other indeterminate moment problems for the continuous $q^{-1}$-Hahn and $q$-Laguerre polynomials.

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Wolter Groenevelt, Erik Koelink. 2009-11-01. The indeterminate moment problem for the $q$-Meixner polynomials. https://doi.org/10.1016/j.jat.2010.07.001

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