Formula:KLS:14.27:19

<< Formula:KLS:14.27:18

formula in Stieltjes-Wigert

Stieltjes-Wigert >>

${\displaystyle{\displaystyle{\displaystyle\lim_{q\rightarrow 1}\frac{\left(q;q\right)_{n}S_{n}\!\left(q^{-1}x\sqrt{2(1-q)}+1;q\right)}{\left(\frac{1-q}{2}\right)^{\frac{n}{2}}}=(-1)^{n}H_{n}\left(x\right)}}}$

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
${\displaystyle{\displaystyle{\displaystyle S_{n}}}}$ : Stieltjes-Wigert polynomial : http://drmf.wmflabs.org/wiki/Definition:StieltjesWigert
${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : Hermite polynomial ${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : http://dlmf.nist.gov/18.3#T1.t1.r28

Bibliography

Equation in Section 14.27 of KLS.

URL links

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