# CAOP

## Graphical Representation of ChebyshevU Polynomials

### Definition

The ChebyshevU polynomials are defined as

\begin{align} U_n(x) &= \sum_{k=0}^{[n/2]} \frac{(-1)^k\,(n-k)!}{k!\,(n-2k)!}\,(2x)^{n-2k}\\ &= (2x)^n {}_2F_1 \left(\left. {-n/2, -n/2+\frac{1}{2} \atop -n} \; \right| \frac{1}{x^2} \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

factor (use Maple-style input)