# Formula:KLS:14.02:12

$\displaystyle {\displaystyle x\monicqRacah{n}@@{x}{\alpha}{\beta}{\gamma}{\delta}{q}=\monicqRacah{n+1}@@{x}{\alpha}{\beta}{\gamma}{\delta}{q}+\left[1+\gamma\delta q-(A_n+C_n)\right]\monicqRacah{n}@@{x}{\alpha}{\beta}{\gamma}{\delta}{q}+A_{n-1}C_n\monicqRacah{n-1}@@{x}{\alpha}{\beta}{\gamma}{\delta}{q} }$

## Substitution(s)

$\displaystyle {\displaystyle C_n=\frac{q(1-q^n)(1-\beta q^n)(\gamma-\alpha\beta q^n)(\delta-\alpha q^n)} {(1-\alpha\beta q^{2n})(1-\alpha\beta q^{2n+1})}}$ &
$\displaystyle {\displaystyle A_n=\frac{(1-\alpha q^{n+1})(1-\alpha\beta q^{n+1})(1-\beta\delta q^{n+1})(1-\gamma q^{n+1})} {(1-\alpha\beta q^{2n+1})(1-\alpha\beta q^{2n+2})}}$

## 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
$\displaystyle {\displaystyle {\widehat R}_{n}}$  : monic $\displaystyle {\displaystyle q}$ -Racah polynomial : http://drmf.wmflabs.org/wiki/Definition:monicqRacah