Formula:KLS:09.02:38

<< Formula:KLS:09.02:37

formula in Racah

Formula:KLS:09.03:01 >>

${\displaystyle{\displaystyle{\displaystyle\Racah{n}@{x(x-N+\delta)}{\alpha}{\beta}{-N-1}{\delta}=\frac{\Wilson{n}@{-(x+\frac{1}{2}(\delta-N))^{2}}{\frac{1}{2}(\delta-N)}{\alpha+1-\frac{1}{2}(\delta-N)}{\beta+\frac{1}{2}(\delta+N)+1}{-\frac{1}{2}(\delta+N)}}{\pochhammer{\alpha+1}{n}\pochhammer{\beta+\delta+1}{n}\pochhammer{-N}{n}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle R_{n}}}}$ : Racah polynomial : http://dlmf.nist.gov/18.25#T1.t1.r4
${\displaystyle{\displaystyle{\displaystyle W_{n}}}}$ : Wilson polynomial : http://dlmf.nist.gov/18.25#T1.t1.r2
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 9.2 of KLS.

URL links

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formula in Racah

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