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Meixner Polynomials
Definition
The Meixner polynomials are defined as
\[
\begin{align}
M_n(x;\beta,c) &= {-\beta \choose n}^{-1} \sum_{k=0}^n {-\beta-x \choose n-k} {x \choose k} \left(\frac{1}{c}\right)^k \\
&= {}_2F_1 \left(\left. {-n, -x \atop \beta} \; \right| 1-\frac{1}{c} \right)
\end{align}
\]
