An algebraic interpretation of the $q$-Meixner polynomials
arXiv:1608.05354 · doi:10.1007/s11139-017-9908-3
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.
19 pages Added AMS classification numbers, a few references and thanks for useful comments on 1st version