Formula:KLS:14.21:16

<< Formula:KLS:14.21:14

formula in q-Laguerre

Formula:KLS:14.21:17 >>

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

Substitution(s)

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

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

${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-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
${\displaystyle{\displaystyle{\displaystyle\mathcal{D}_{q}^{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-derivative : http://drmf.wmflabs.org/wiki/Definition:qderiv

Bibliography

Equation in Section 14.21 of KLS.

URL links

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

<< Formula:KLS:14.21:14

formula in q-Laguerre

Formula:KLS:14.21:17 >>