Definition:AlSalamCarlitzII

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The LaTeX DLMF and DRMF macro \AlSalamCarlitzII represents the Al-Salam-Carlitz II polynomial.

This macro is in the category of polynomials.

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

\AlSalamCarlitzII{a}{n} produces ${\displaystyle{\displaystyle{\displaystyle V^{(a)}_{n}}}}$

\AlSalamCarlitzII{a}{n}@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle V^{(a)}_{n}\!\left(x;q\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle V^{(a)}_{n}\!\left(x;q\right):=(-a)^{n}q^{-\genfrac{(}{)}{0.0pt}{}{n}{2}}\,\qHyperrphis{2}{0}@@{q^{-n},x}{-}{q}{\frac{q^{n}}{a}}.}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle V^{(n)}_{\alpha}}}}$ : Al-Salam-Carlitz II polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzII
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#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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