Definition:StieltjesWigert

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The LaTeX DLMF and DRMF macro \StieltjesWigert represents the Stieltjes Wigert polynomial.

This macro is in the category of polynomials.

In math mode, this macro can be called in the following ways:

\StieltjesWigert{n} produces ${\displaystyle{\displaystyle{\displaystyle S_{n}}}}$

\StieltjesWigert{n}@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle S_{n}\!\left(x;q\right)}}}$

\StieltjesWigert{n}@@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle S_{n}\!\left(x\right)}}}$

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

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

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