Formula:KLS:14.27:14

<< Formula:KLS:14.27:13

formula in Stieltjes-Wigert

Formula:KLS:14.27:15 >>

${\displaystyle{\displaystyle{\displaystyle\left(t;q\right)_{\infty}\cdot\qHyperrphis{0}{2}@@{-}{0,t}{q}{-qxt}=\sum_{n=0}^{\infty}(-1)^{n}q^{\binomial{n}{2}}S_{n}\!\left(x;q\right)t^{n}}}}$

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
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle S_{n}}}}$ : Stieltjes-Wigert polynomial : http://drmf.wmflabs.org/wiki/Definition:StieltjesWigert

Bibliography

Equation in Section 14.27 of KLS.

URL links

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<< Formula:KLS:14.27:13

formula in Stieltjes-Wigert

Formula:KLS:14.27:15 >>