Definition:ctsqHermite

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

This macro is in the category of polynomials.

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

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

\ctsqHermite{n}@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle H_{n}\!\left(x\,|\,q\right)}}}$

\ctsqHermite{n}@@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle H_{n}\!\left(x\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle H_{n}\!\left(x\,|\,q\right):={\mathrm{e}^{in\theta}}\,\qHyperrphis{2}{0}@@{q^{-n},0}{-}{q}{q^{n}{\mathrm{e}^{-2i\theta}}}}}}$

Symbols List

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

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