# CAOP

## Graphical Representation of 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}

### Plot

Note: You can choose a selection on the small graph in order to zoom. Mark the check boxes on the left side for which n you want to plot the graph.

### Parameters

Parameters

$$\beta$$ $$\beta > 0$$

$$c$$ $$0 < c < 1$$

factor (use Maple-style input)