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Hahn Polynomials
Definition
The Hahn polynomials are defined as
\[
\begin{align}
Q_n(x;\alpha,\beta,N) &= \sum_{k=0}^n \frac{(-n)_k (n+\alpha+\beta+1)_k (-x)_k}{(\alpha+1)_k (-N)_k k!}\\
&= {}_3F_2 \left(\left. {-n, n+\alpha+\beta+1, -x \atop \alpha+1, -N} \; \right| 1 \right)
\end{align}
\]
