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This article is cited in 6 scientific papers (total in 6 papers)
On the $q$-Charlier Multiple Orthogonal Polynomials
Jorge Arvesú, Andys M. Ramírez-Aberasturis Department of Mathematics, Universidad Carlos III de Madrid,
Avenida de la Universidad, 30, 28911, Leganés, Spain
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.
Keywords:
multiple orthogonal polynomials; Hermite–Padé approximation; difference equations; classical orthogonal polynomials of a discrete variable; Charlier polynomials; $q$-polynomials.
Received: November 10, 2014; in final form March 23, 2015; Published online March 28, 2015
Citation:
Jorge Arvesú, Andys M. Ramírez-Aberasturis, “On the $q$-Charlier Multiple Orthogonal Polynomials”, SIGMA, 11 (2015), 026, 14 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1007 https://www.mathnet.ru/eng/sigma/v11/p26
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