Formula:KLS:14.21:27

<< Formula:KLS:14.21:26

formula in q-Laguerre

Formula:KLS:14.21:28 >>

${\displaystyle{\displaystyle{\displaystyle L^{(\alpha)}_{n}\!\left(x;q^{-1}\right)=\frac{\left(q^{\alpha+1};q\right)_{n}}{\left(q;q\right)_{n}q^{n\alpha}}p_{n}\!\left(-x;q^{\alpha};q\right)}}}$

Proof

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

Bibliography

Equation in Section 14.21 of KLS.

URL links

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<< Formula:KLS:14.21:26

formula in q-Laguerre

Formula:KLS:14.21:28 >>