Formula:KLS:14.27:01

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formula in Stieltjes-Wigert

Formula:KLS:14.27:02 >>

${\displaystyle{\displaystyle{\displaystyle S_{n}\!\left(x;q\right)=\frac{1}{\left(q;q\right)_{n}}\,\qHyperrphis{1}{1}@@{q^{-n}}{0}{q}{-q^{n+1}x}}}}$

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
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

Bibliography

Equation in Section 14.27 of KLS.

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<< Continuous q-Hermite

formula in Stieltjes-Wigert

Formula:KLS:14.27:02 >>