Formula:KLS:14.27:05

<< Formula:KLS:14.27:04

formula in Stieltjes-Wigert

Formula:KLS:14.27:06 >>

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

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle S_{n}}}}$ : Stieltjes-Wigert polynomial : http://drmf.wmflabs.org/wiki/Definition:StieltjesWigert
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{\widehat{S}}_{n}}}}$ : monic Stieltjes-Wigert polynomial : http://drmf.wmflabs.org/wiki/Definition:monicStieltjesWigert

Bibliography

Equation in Section 14.27 of KLS.

URL links

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<< Formula:KLS:14.27:04

formula in Stieltjes-Wigert

Formula:KLS:14.27:06 >>