Hahn Polynomials - Orthogonality

Orthogonality

where δ_x,y is the Kronecker delta function and the weight functions are

and

$\pi_n=\pi_n(\alpha,\beta,N)=\frac{N-1}{n}\frac{2n+\alpha+\beta+1}{\alpha+\beta+1} \frac{\Gamma(\beta+1,n+\alpha+1,n+\alpha+\beta+1)}{\Gamma(\alpha+1,\alpha+\beta+1,n+\beta+1,n+1)}/\binom{N+\alpha+\beta+n}{n}$ .

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