Formula:KLS:14.20:28

<< Formula:KLS:14.20:27

formula in Little q-Laguerre / Wall

Formula:KLS:14.21:01 >>

${\displaystyle{\displaystyle{\displaystyle xp_{n}\!\left(x^{2};q;q^{2}\right)=\frac{(-1)^{n}q^{-n(n-1)}}{\left(q^{3};q^{2}\right)_{n}}h_{2n+1}\!\left(x;q\right)}}}$

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

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : 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

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

<< Formula:KLS:14.20:27

formula in Little q-Laguerre / Wall

Formula:KLS:14.21:01 >>