%0 Journal Article
%T On the $q$-Charlier Multiple Orthogonal Polynomials
%A Jorge Arves¨˛
%A Andys M. Ram¨Ērez-Aberasturis
%J Mathematics
%D 2014
%I arXiv
%R 10.3842/SIGMA.2015.026
%X 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.
%U http://arxiv.org/abs/1411.2000v2