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Continuous Dual Hahn Polynomials
Definition
The Continuous Dual Hahn polynomials are defined as
\[
\begin{align}
S_n(x^2;a,b,c) &= (a+b)_n (a+c)_n \sum_{k=0}^n \frac{(-n)_k (a+i x)_k (a-i x)_k}{(a+b)_k (a+c)_k k!}\\
&= (a+b)_n (a+c)_n {}_3F_2 \left(\left. {-n, a+i x, a-i x \atop a+b, a+c} \; \right| 1 \right)
\end{align}
\]
