Formula:KLS:14.20:27

<< Formula:KLS:14.20:26

formula in Little q-Laguerre / Wall

Little q-Laguerre / Wall >>

${\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x^{2};q^{-1};q^{2}\right)=\frac{(-1)^{n}q^{-n(n-1)}}{\left(q;q^{2}\right)_{n}}h_{2n}\!\left(x;q\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle h_{n}}}}$ : discrete ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hermite I polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteI

Bibliography

Equation in Section 14.20 of KLS.

URL links

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<< Formula:KLS:14.20:26

formula in Little q-Laguerre / Wall

Little q-Laguerre / Wall >>