Formula:KLS:14.02:12

<< Formula:KLS:14.02:09

formula in q-Racah

Formula:KLS:14.02:13 >>

${\displaystyle{\displaystyle{\displaystyle x{\widehat{R}}_{n}\!\left(x\right)={\widehat{R}}_{n+1}\!\left(x\right)+\left[1+\gamma\delta q-(A_{n}+C_{n})\right]{\widehat{R}}_{n}\!\left(x\right)+A_{n-1}C_{n}{\widehat{R}}_{n-1}\!\left(x\right)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle C_{n}=\frac{q(1-q^{n})(1-\beta q^{n})(\gamma-\alpha\beta q^{n})(\delta-\alpha q^{n})}{(1-\alpha\beta q^{2n})(1-\alpha\beta q^{2n+1})}}}}$ &
${\displaystyle{\displaystyle{\displaystyle A_{n}=\frac{(1-\alpha q^{n+1})(1-\alpha\beta q^{n+1})(1-\beta\delta q^{n+1})(1-\gamma q^{n+1})}{(1-\alpha\beta q^{2n+1})(1-\alpha\beta q^{2n+2})}}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle{\widehat{R}}_{n}}}}$ : monic ${\displaystyle{\displaystyle{\displaystyle q}}}$-Racah polynomial : http://drmf.wmflabs.org/wiki/Definition:monicqRacah

Bibliography

Equation in Section 14.2 of KLS.

URL links

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<< Formula:KLS:14.02:09

formula in q-Racah

Formula:KLS:14.02:13 >>