Formula:KLS:14.06:09

<< Formula:KLS:14.06:08

formula in q-Hahn

Formula:KLS:14.06:13 >>

${\displaystyle{\displaystyle{\displaystyle q^{-n}(1-q^{n})(1-\alpha\beta q^{n+1})y(x){}=B(x)y(x+1)-\left[B(x)+D(x)\right]y(x)+D(x)y(x-1)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle D(x)=\alpha q(1-q^{x})(\beta-q^{x-N-1})}}}$ &

${\displaystyle{\displaystyle{\displaystyle B(x)=(1-q^{x-N})(1-\alpha q^{x+1})}}}$ &

${\displaystyle{\displaystyle{\displaystyle y(x)=Q_{n}\!\left(q^{-x};\alpha,\beta,N;q\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle Q_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:qHahn

Bibliography

Equation in Section 14.6 of KLS.

URL links

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

<< Formula:KLS:14.06:08

formula in q-Hahn

Formula:KLS:14.06:13 >>