# Formula:KLS:14.07:30

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$\displaystyle {\displaystyle \lim_{q\rightarrow 1}\dualqHahn{n}@{\mu(x)}{q^{\gamma}}{q^{\delta}}{N}{q}=\dualHahn{n}@{\lambda(x)}{\gamma}{\delta}{N} }$

## Substitution(s)

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

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

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

## Proof

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## Symbols List

& : logical and
$\displaystyle {\displaystyle R_{n}}$  : dual $\displaystyle {\displaystyle q}$ -Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:dualqHahn
$\displaystyle {\displaystyle R_{n}}$  : dual Hahn polynomial : http://dlmf.nist.gov/18.25#T1.t1.r5

## URL links

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