Formula:KLS:14.02:50

<< Formula:KLS:14.02:49

formula in q-Racah

Formula:KLS:14.02:51 >>

${\displaystyle{\displaystyle{\displaystyle R_{n}\!\left(x;\alpha,\beta,q^{-N-1},-1\,|\,q\right)=\frac{\left(\beta q,-\alpha q;q\right)_{n}}{\left(\alpha q,-\beta q;q\right)_{n}}(-1)^{n}R_{n}\!\left(-x;\beta,\alpha,q^{-N-1},-1\,|\,q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle R_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Racah polynomial : http://dlmf.nist.gov/18.28#E19
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.2 of KLS.

URL links

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<< Formula:KLS:14.02:49

formula in q-Racah

Formula:KLS:14.02:51 >>