Formula:KLS:09.05:29

<< Formula:KLS:09.05:28

formula in Hahn

Formula:KLS:09.05:30 >>

${\displaystyle{\displaystyle{\displaystyle\sum_{n=0}^{N}\frac{(2n+\alpha+\beta+1){\left(\alpha+1\right)_{n}}{\left(-N\right)_{n}}N!}{(-1)^{n}{\left(n+\alpha+\beta+1\right)_{N+1}}{\left(\beta+1\right)_{n}}n!}Q_{n}\!\left(x;\alpha,\beta,N\right)Q_{n}\!\left(y;\alpha,\beta,N\right){}=\frac{\delta_{x,y}}{\dbinom{\alpha+x}{x}\dbinom{\beta+N-x}{N-x}}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle x,y\in\{0,1,2,\ldots,N\}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle Q_{n}}}}$ : Hahn polynomial : http://dlmf.nist.gov/18.19#T1.t1.r3
${\displaystyle{\displaystyle{\displaystyle\delta_{m,n}}}}$ : Kronecker delta : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4
${\displaystyle{\displaystyle{\displaystyle\in}}}$ : element of : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r9

Bibliography

Equation in Section 9.5 of KLS.

URL links

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<< Formula:KLS:09.05:28

formula in Hahn

Formula:KLS:09.05:30 >>