# CAOP

## Graphical Representation of Laguerre Polynomials

### Definition

The Laguerre polynomials are defined as

\begin{align} L_n^{(\alpha)}(x) &= \sum_{k=0}^n {n+\alpha \choose n-k} \frac{1}{k!} \left(-x\right)^k\\ &= \frac{(\alpha+1)_n}{n!} {}_1F_1 \left(\left. {-n \atop \alpha+1} \; \right| x \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

$$\alpha$$ $$\alpha > -1$$

factor (use Maple-style input)