Formula:KLS:14.07:04

<< Formula:KLS:14.07:03

formula in Dual q-Hahn

Formula:KLS:14.07:05 >>

${\displaystyle{\displaystyle{\displaystyle-\left(1-q^{-x}\right)\left(1-\gamma\delta q^{x+1}\right)R_{n}\!\left(\mu(x)\right){q}{}=A_{n}R_{n+1}\!\left(\mu(x)\right){q}-\left(A_{n}+C_{n}\right)R_{n}\!\left(\mu(x)\right){q}+C_{n}R_{n-1}\!\left(\mu(x)\right){q}}}}$

Substitution(s)

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

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

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

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
${\displaystyle{\displaystyle{\displaystyle R_{n}}}}$ : dual ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:dualqHahn

Bibliography

Equation in Section 14.7 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:14.07:03

formula in Dual q-Hahn

Formula:KLS:14.07:05 >>