Q-Meixner polynomials
# Q-Meixner polynomials

In mathematics, the q-Meixner polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

## Definition

The polynomials are given in terms of basic hypergeometric functions by

    $M_{n}(q^{-x};b,c;q)=_{2}\phi _{1}\left[{\begin{matrix}q^{-n},q^{-x}\\bq\end{matrix}};q,-{\frac {q^{n+1}}{c}}\right].$
