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arXiv · 1411.2000

On the $q$-Charlier Multiple Orthogonal Polynomials

Jorge Arvesú·Andys M. Ramírez-Aberasturis
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Abstract

We introduce a new family of special functions, namely $q$-Charlier multiple orthogonal polynomials. These polynomials are orthogonal with respect to $q$-analogues of Poisson distributions. We focus our attention on their structural properties. Raising and lowering operators as well as Rodrigues-type formulas are obtained. An explicit representation in terms of a $q$-analogue of the second of Appell's hypergeometric functions is given. A high-order linear $q$-difference equation with polynomial coefficients is deduced. Moreover, we show how to obtain the nearest neighbor recurrence relation from some difference operators involved in the Rodrigues-type formula.

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BibTeXRIS

Jorge Arvesú, Andys M. Ramírez-Aberasturis. 2014-11-07. On the $q$-Charlier Multiple Orthogonal Polynomials. https://doi.org/10.3842/sigma.2015.026

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