On the $q$-Charlier Multiple Orthogonal Polynomials
Classical Analysis and ODEs
2015-03-31 v2
Abstract
We introduce a new family of special functions, namely -Charlier multiple orthogonal polynomials. These polynomials are orthogonal with respect to -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 -analogue of the second of Appell's hypergeometric functions is given. A high-order linear -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.
Cite
@article{arxiv.1411.2000,
title = {On the $q$-Charlier Multiple Orthogonal Polynomials},
author = {Jorge Arvesú and Andys M. Ramírez-Aberasturis},
journal= {arXiv preprint arXiv:1411.2000},
year = {2015}
}