## An algebraic interpretation of the $q$-Meixner polynomials

### Abstract

An algebraic interpretation of the $q$-Meixner polynomials is obtained. It is based on representations of $\mathcal{U}_q(\mathfrak{su}(1,1))$ on $q$-oscillator states with the polynomials appearing as matrix elements of unitary $q$-pseudorotation operators. These operators are built from $q$-exponentials of the $\mathcal{U}_q(\mathfrak{su}(1,1))$ generators. The orthogonality, recurrence relation, difference equation, and other properties of the $q$-Mexiner polynomials are systematically obtained in the proposed framework.Comment: 19 pages Added AMS classification numbers, a few references and thanks for useful comments on 1st versio

Topics: Mathematical Physics, Mathematics - Classical Analysis and ODEs, 33D45, 81R50
Publisher: 'Springer Science and Business Media LLC'
Year: 2017
DOI identifier: 10.1007/s11139-017-9908-3
OAI identifier: oai:arXiv.org:1608.05354

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