CAOP

Equations

Graphical Representation of Wilson Polynomials

Definition

The Wilson polynomials are defined as

\[ \begin{align} W_n(x^2;a,b,c,d) &= (a+b)_n (a+c)_n (a+d)_n \sum_{k=0}^n \frac{(-n)_k (n+a+b+c+d-1)_k (a+i x)_k (a-i x)_k}{(a+b)_k (a+c)_k (a+d)_k k!}\\ &= (a+b)_n (a+c)_n (a+d)_n {}_4F_3 \left(\left. {-n, n+a+b+c+d-1, a+i x, a-i x\atop a+b, a+c, a+d} \; \right| 1 \right) \end{align} \]

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

\(a\) \(\)

\(b\) \(\)

\(c\) \(\)

\(d\) \(\)

factor (use Maple-style input)