# CAOP

## Graphical Representation of Dual Hahn Polynomials

### Definition

The Dual Hahn polynomials are defined as

\begin{align} R_n(\lambda(x);\gamma,\delta,N) &= \sum_{k=0}^n \frac{(-n)_k (-x)_k (x+\gamma+\delta+1)_k}{(\gamma+1)_k (-N)_k k!}\\ &= {}_3F_2 \left(\left. {-n, -x, x+\gamma+\delta+1 \atop \gamma+1, -N} \; \right| 1 \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

$$\gamma$$ $$\gamma > -1$$

$$\delta$$ $$\delta > -1$$

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

factor (use Maple-style input)