Formula:KLS:14.21:14

<< Formula:KLS:14.21:13

formula in q-Laguerre

Formula:KLS:14.21:16 >>

${\displaystyle{\displaystyle{\displaystyle\mathcal{D}_{q}\left[w(x;\alpha;q)L^{(\alpha)}_{n}\!\left(x;q\right)\right]=\frac{1-q^{n+1}}{1-q}w(x;\alpha-1;q)L^{(\alpha-1)}_{n+1}\!\left(x;q\right)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle w(x;\alpha;q)=\frac{x^{\alpha}}{\left(-x;q\right)_{\infty}}}}}$

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
${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:qLaguerre
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.21 of KLS.

URL links

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<< Formula:KLS:14.21:13

formula in q-Laguerre

Formula:KLS:14.21:16 >>