q-Meixner polynomials

Not to be confused with q-Meixner–Pollaczek 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

$M_n(q^{-x};b,c;q)={}_2{\varphi }_1[\begin{array}{c}{q}^{-n},q^{-x}\\ bq\end{array};q,-\frac{q^{n+1}}{c}].$

References

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