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