Formula:KLS:14.20:26

<< Formula:KLS:14.20:25

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:27 >>

${\displaystyle{\displaystyle{\displaystyle x^{n}=\left(a;q\right)_{n}\sum_{k=0}^{n}\frac{\left(q^{-n};q\right)_{k}}{\left(q;q\right)_{k}}q^{nk}p_{k}\!\left(x;a;q\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre / Wall polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqLaguerre

Bibliography

Equation in Section 14.20 of KLS.

URL links

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<< Formula:KLS:14.20:25

formula in Little q-Laguerre / Wall

Formula:KLS:14.20:27 >>