# Formula:KLS:14.02:37

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$\displaystyle {\displaystyle \qRacah{n}@{\mu(x)}{\alpha}{0}{q^{-N-1}}{\alpha\delta q^{N+1}}{q}=\dualqHahn{n}@{{\tilde \mu}(x)}{\alpha}{\delta}{N}{q} }$

## Substitution(s)

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

$\displaystyle {\displaystyle \mu(x)=q^{-x}+\gamma\delta q^{x+1} =\lambda(x)=q^{-x}+cq^{x-N} =q^{-x}+q^{x+\gamma+\delta+1} =2a\cos@@{\theta}}$ &
$\displaystyle {\displaystyle \lambda(x)=x(x+\gamma+\delta+1)}$ &
$\displaystyle {\displaystyle \mu(x):=q^{-x}+\gamma\delta q^{x+1}}$ &
$\displaystyle {\displaystyle \mu(x)=q^{-x}+\gamma\delta q^{x+1} =\lambda(x)=q^{-x}+cq^{x-N} =q^{-x}+q^{x+\gamma+\delta+1} =2a\cos@@{\theta}}$ &

$\displaystyle {\displaystyle \lambda(x)=x(x+\gamma+\delta+1)}$

## Proof

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## Symbols List

& : logical and
$\displaystyle {\displaystyle R_{n}}$  : $\displaystyle {\displaystyle q}$ -Racah polynomial : http://dlmf.nist.gov/18.28#E19
$\displaystyle {\displaystyle R_{n}}$  : dual $\displaystyle {\displaystyle q}$ -Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:dualqHahn
$\displaystyle {\displaystyle \mathrm{cos}}$  : cosine function : http://dlmf.nist.gov/4.14#E2

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