Δ-Meixner–Sobolev orthogonal polynomials: Mehler–Heine type formula and zeros

摘要

We provide a Mehler–Heine type formula for a nonstandard family of discrete orthogonal polynomials. Concretely, we consider the Δ-Meixner–Sobolev polynomials which are orthogonal with respect to an inner product involving the Pascal distribution and the forward difference operator. Consequences on the zeros of these polynomials are analyzed and illustrated numerically.