Formula:KLS:14.02:46

<< Formula:KLS:14.02:42

formula in q-Racah

Formula:KLS:14.02:47 >>

${\displaystyle{\displaystyle{\displaystyle R_{n}\!\left(2a\cos\theta;abq^{-1},cdq^{-1},adq^{-1},ad^{-1}\,|\,q\right)=\frac{a^{n}p_{n}\!\left(x;a,b,c,d\,|\,q\right)}{\left(ab,ac,ad;q\right)_{n}}}}}$

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
${\displaystyle{\displaystyle{\displaystyle\mathrm{cos}}}}$ : cosine function : http://dlmf.nist.gov/4.14#E2
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : Askey-Wilson polynomial : http://dlmf.nist.gov/18.28#E1
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-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:14.02:42

formula in q-Racah

Formula:KLS:14.02:47 >>