Definition:discrqHermiteII

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The LaTeX DLMF and DRMF macro \discrqHermiteII represents the second discrete ${\displaystyle{\displaystyle q}}$ Hermite polynomial.

This macro is in the category of polynomials.

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

\discrqHermiteII{n} produces ${\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}}}}$

\discrqHermiteII{n}@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}\!\left(x;q\right)}}}$

\discrqHermiteII{n}@@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}\!\left(x\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}\!\left(x;q\right):=i^{-n}V^{(-1)}_{n}\!\left(ix;q\right)}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle\tilde{h}_{n}}}}$ : discrete ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hermite II polynomial : http://drmf.wmflabs.org/wiki/Definition:discrqHermiteII
${\displaystyle{\displaystyle{\displaystyle V^{(n)}_{\alpha}}}}$ : Al-Salam-Carlitz II polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzII

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