CAOP

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Dual Hahn Polynomials

Definition

The Dual Hahn polynomials are defined as

\[ \begin{align} R_n(\lambda(x);\gamma,\delta,N) &= \sum_{k=0}^n \frac{(-n)_k (-x)_k (x+\gamma+\delta+1)_k}{(\gamma+1)_k (-N)_k k!}\\ &= {}_3F_2 \left(\left. {-n, -x, x+\gamma+\delta+1 \atop \gamma+1, -N} \; \right| 1 \right) \end{align} \]

Difference Equation

Recurrence Equation

Parameters

Variables

\(n\)

\(x\)

Parameters

\(\gamma\) \(\gamma > -1\)

\(\delta\) \(\delta > -1\)

\(N\) \(N > 0\)

factor (use Maple-style input)

   hypergeometric term in \(n\) and hypergeometric term in \(x\) required