Meixner $d$-Orthogonal Polynomials Arising from $\mathfrak{su}(1,1)$

Abstract

In this study, we present a novel family of Meixner-type $d$-orthogonal polynomials, which are distinguished as a particular subset of multiple orthogonal polynomials. We demonstrate their connection to the Lie algebra $\mathfrak{su}(1,1)$ by identifying them as matrix elements of an appropriately defined nonlinear operator. Utilizing Barut-Girardello coherent states, we explicitly outline their key features, including recurrence relations, generating functions, and $d$-orthogonality relations, among others.