Definition:ctsbigqHermite

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The LaTeX DLMF and DRMF macro \ctsbigqHermite represents continuous big ${\displaystyle{\displaystyle q}}$-Hermite polynomial.

This macro is in the category of polynomials.

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

\ctsbigqHermite{n} produces ${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$

\ctsbigqHermite{n}@{x}{a}{q} produces ${\displaystyle{\displaystyle{\displaystyle H_{n}\!\left(x;a|q\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle H_{n}\!\left(x;a|q\right):=a^{-n}\,\qHyperrphis{3}{2}@@{q^{-n},a{\mathrm{e}^{i\theta}},a{\mathrm{e}^{-i\theta}}}{0,0}{q}{q}.}}\)\@add@PDF@RDFa@triples\end{document}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle H_{n}}}}$ : continuous big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hermite polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsbigqHermite
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11

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