# Formula:KLS:14.17:22

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

## Substitution(s)

$\displaystyle {\displaystyle \lambda(n)=q^{-n}-pq^n}$ &

$\displaystyle {\displaystyle \lambda(x)=q^{-x}+cq^{x-N}}$ &
$\displaystyle {\displaystyle \mu(x)=\lambda(x)=q^{-x}+cq^{x-N}}$ &
$\displaystyle {\displaystyle \lambda(n)=q^{-n}-pq^n}$ &
$\displaystyle {\displaystyle \lambda(x)=q^{-x}+cq^{x-N}}$ &
$\displaystyle {\displaystyle \lambda(x):=q^{-x}+cq^{x-N}}$ &
$\displaystyle {\displaystyle \lambda(n)=q^{-n}-pq^n}$ &

$\displaystyle {\displaystyle \lambda(x)=q^{-x}+cq^{x-N}}$

## 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
$\displaystyle {\displaystyle R_{n}}$  : $\displaystyle {\displaystyle q}$ -Racah polynomial : http://dlmf.nist.gov/18.28#E19
$\displaystyle {\displaystyle K_{n}}$  : dual $\displaystyle {\displaystyle q}$ -Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:dualqKrawtchouk