On the q-Charlier Multiple Orthogonal Polynomials

被引：7

作者：

Arvesu, Jorge ^{[1
]}

Ramirez-Aberastruris, Andys M. ^{[1
]}

机构：

[1] Univ Carlos III Madrid, Dept Math, Leganes 28911, Spain

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2015年 / 11卷

关键词：

multiple orthogonal polynomials; Hermite-Pade approximation; difference equations; classical orthogonal polynomials of a discrete variable; Charlier polynomials; q-polynomials; ASYMPTOTICS; ZEROS;

D O I：

10.3842/SIGMA.2015.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：14

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