Formula:KLS:14.05:13

<< Formula:KLS:14.05:12

formula in Big q-Jacobi

Formula:KLS:14.05:14 >>

${\displaystyle{\displaystyle{\displaystyle\mathcal{D}_{q}P_{n}\!\left(x;a,b,c;q\right)=\frac{q^{-n+1}(1-q^{n})(1-abq^{n+1})}{(1-q)(1-aq)(1-cq)}P_{n-1}\!\left(qx;aq,bq,cq;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathcal{D}_{q}^{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-derivative : http://drmf.wmflabs.org/wiki/Definition:qderiv
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqJacobi

Bibliography

Equation in Section 14.5 of KLS.

URL links

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<< Formula:KLS:14.05:12

formula in Big q-Jacobi

Formula:KLS:14.05:14 >>