Nearest neighbor recurrence relations for Meixner-Angelesco multiple orthogonal polynomials of the second kind

Abstract

This paper studies a new family of Angelesco multiple orthogonal polynomials with shared orthogonality conditions with respect to a system of weight functions, which are complex analogues of Pascal distributions on a legged star-like set. The emphasis is placed on the algebraic properties such as the raising operators, the Rodrigues-type formula, the explicit expression of the polynomials, and the nearest neighbor recurrence relations.