Formula:KLS:14.20:08

<< Formula:KLS:14.20:07

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:09 >>

${\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x;a;q\right)=\frac{(-1)^{n}q^{-\binomial{n}{2}}}{\left(aq;q\right)_{n}}{\widehat{p}}_{n}\!\left(x\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre / Wall polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqLaguerre
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{\widehat{p}}_{n}}}}$ : monic little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre/Wall polynomial : http://drmf.wmflabs.org/wiki/Definition:moniclittleqLaguerre

Bibliography

Equation in Section 14.20 of KLS.

URL links

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<< Formula:KLS:14.20:07

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:09 >>