CAOP

Equations

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)