An Algebraic Model for the Multiple Meixner Polynomials of the First Kind
Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
TL;DR
This paper introduces an algebraic framework using Lie algebras and oscillator operators to interpret and analyze the properties of multiple Meixner polynomials of the first kind.
Contribution
It provides a novel algebraic model that offers new insights into the structure and properties of these orthogonal polynomials.
Findings
Derived properties of multiple Meixner polynomials using the algebraic model
Connected orthogonal polynomials with Lie algebra representations
Enhanced understanding of polynomial behavior through oscillator operators
Abstract
An interpretation of the multiple Meixner polynomials of the first kind is provided through an infinite Lie algebra realized in terms of the creation and annihilation operators of a set of independent oscillators. The model is used to derive properties of these orthogonal polynomials.
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