Formula:KLS:14.06:24

<< Formula:KLS:14.06:23

formula in q-Hahn

Formula:KLS:14.06:25 >>

${\displaystyle{\displaystyle{\displaystyle R_{n}\!\left(\mu(x);q^{-N-1},\beta\gamma q^{N+1},\gamma,0\,|\,q\right)=Q_{n}\!\left(q^{-x};\gamma,\beta,N;q\right)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle\mu(n)=q^{-n}+\alpha\beta q^{n+1}}}}$ &
${\displaystyle{\displaystyle{\displaystyle\mu(x)=q^{-x}+\gamma\delta q^{x+1}}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle R_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Racah polynomial : http://dlmf.nist.gov/18.28#E19
${\displaystyle{\displaystyle{\displaystyle Q_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:qHahn

Bibliography

Equation in Section 14.6 of KLS.

URL links

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<< Formula:KLS:14.06:23

formula in q-Hahn

Formula:KLS:14.06:25 >>