Definition:ctsqHermite

The LaTeX DLMF and DRMF macro \ctsqHermite represents the continuous ${\displaystyle q}$-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 $\displaystyle {\displaystyle \ctsqHermite{n}}$
\ctsqHermite{n}@{x}{q} produces $\displaystyle {\displaystyle \ctsqHermite{n}@{x}{q}}$
\ctsqHermite{n}@@{x}{q} produces $\displaystyle {\displaystyle \ctsqHermite{n}@@{x}{q}}$

These are defined by $\displaystyle {\displaystyle \ctsqHermite{n}@{x}{q}:=\expe^{in\theta}\,\qHyperrphis{2}{0}@@{q^{-n},0}{-}{q}{q^n\expe^{-2i\theta}} }$

Symbols List

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