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 analogs 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.

Keywords

• Angelesco polynomials
• classical orthogonal polynomials
• discrete orthogonal polynomials
• multiple orthogonal polynomials
• Meixner polynomials
• Rodrigues-type formula