# CAOP

## Graphical Representation of Krawtchouk Polynomials

### Definition

The Krawtchouk polynomials are defined as

\begin{align} K_n(x;p,N) &= {N \choose n}^{-1} \sum_{k=0}^n {N-x \choose n-k} {x \choose k} \left(1-\frac{1}{p}\right)^k\\ &= {}_2F_1 \left(\left. {-n, -x \atop -N} \; \right| \frac{1}{p} \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

$$p$$ $$0 < p < 1$$

$$N$$ $$N > 0$$

factor (use Maple-style input)