Formula:KLS:14.12:13

<< Formula:KLS:14.12:12

formula in Little q-Jacobi

Formula:KLS:14.12:14 >>

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

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
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqJacobi

Bibliography

Equation in Section 14.12 of KLS.

URL links

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<< Formula:KLS:14.12:12

formula in Little q-Jacobi

Formula:KLS:14.12:14 >>