d-Orthogonal polynomials and su(2)

TL;DR

This paper identifies and characterizes two families of d-orthogonal polynomials associated with the su(2) algebra, revealing their algebraic properties and their limits to classical polynomials under algebra contraction.

Contribution

It provides a full algebraic characterization of these new polynomial families, including explicit formulas, recurrence relations, and generating functions.

Findings

Polynomials tend to Meixner and d-Charlier polynomials in the contraction limit.

Explicit expressions and recurrence relations are derived.

The algebraic setting facilitates their complete characterization.

Abstract

Two families of d-orthogonal polynomials related to su(2) are identified and studied. The algebraic setting allows their full characterization (explicit expressions, recurrence relations, difference equations, generating functions, etc.) of those polynomials. In the limit where su(2) contracts to the Heisenberg-Weyl algebra h_1, these polynomials tend to the standard Meixner polynomials and d-Charlier polynomials, respectively.