Formula:KLS:14.07:26

<< Formula:KLS:14.07:25

formula in Dual q-Hahn

Formula:KLS:14.07:28 >>

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

Substitution(s)

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

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

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

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
${\displaystyle{\displaystyle{\displaystyle R_{n}}}}$ : dual ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:dualqHahn

Bibliography

Equation in Section 14.7 of KLS.

URL links

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<< Formula:KLS:14.07:25

formula in Dual q-Hahn

Formula:KLS:14.07:28 >>