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arXiv · 1804.11171

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

Borhen Halouani·Fethi Bouzeffour
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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.

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Borhen Halouani, Fethi Bouzeffour. 2024-04-27. Meixner $d$-Orthogonal Polynomials Arising from $\mathfrak{su}(1,1)$. https://arxiv.org/abs/1804.11171

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