# Formula:KLS:14.07:29

$\displaystyle {\displaystyle \lim_{\gamma\rightarrow 0} \dualqHahn{n}@{\mu(x)}{\gamma}{c\gamma^{-1}q^{-N-1}}{N}{q}=\dualqKrawtchouk{n}@{\lambda(x)}{c}{N}{q} }$

## 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

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

## Symbols List

& : logical and
$\displaystyle {\displaystyle R_{n}}$  : dual $\displaystyle {\displaystyle q}$ -Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:dualqHahn
$\displaystyle {\displaystyle K_{n}}$  : dual $\displaystyle {\displaystyle q}$ -Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:dualqKrawtchouk