Asymptotics for the ratio and the zeros of multiple Charlier polynomials

We investigate multiple Charlier polynomials and in particular we will use the (nearest neighbor) recurrence relation to find the asymptotic behavior of the ratio of two multiple Charlier polynomials. This result is then used to obtain the asymptotic distribution of the zeros, which is uniform on an interval. We also deal with the case where one of the parameters of the various Poisson distributions depend on the degree of the polynomial, in which case we obtain another asymptotic distribution of the zeros.Comment: 19 pages, 3 figure

On the q-Charlier Multiple Orthogonal Polynomials

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.The research of J. Arves u was partially supported by the research grant MTM2012-36732-C03-01 (Ministerio de Econom a y Competitividad) of Spain