On two families of discrete multiple orthogonal polynomials on a star-like set

We study two families of type II discrete multiple orthogonal polynomials on an r-legged star-like set with respect to r weight functions of Charlier (Poisson distributions) and Meixner (negative binomial distributions), respectively. We focus our attention on the structural properties such as the raising operators, the Rodrigues-type formulas, and the explicit expressions of the polynomial families as well as the coefficients of the nearest neighbor recurrence relation. A limit relation between these families is given.

multiple orthogonal polynomials; charlier-angelesco polynomials; meixner-angelesco polynomials; rodrigues-type formula; recurrence relation

On two families of discrete multiple orthogonal polynomials on a star-like set Articles