Definition:AlSalamCarlitzI

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Definition:AlSalamCarlitzII >>

The LaTeX DLMF and DRMF macro \AlSalamCarlitzI represents the Al-Salam-Carlitz I polynomial.

This macro is in the category of polynomials.

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

\AlSalamCarlitzI{a}{n} produces ${\displaystyle{\displaystyle{\displaystyle U^{(a)}_{n}}}}$

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

These are defined by ${\displaystyle{\displaystyle{\displaystyle U^{(a)}_{n}\!\left(x;q\right):=(-a)^{n}q^{\genfrac{(}{)}{0.0pt}{}{n}{2}}\,\qHyperrphis{2}{1}@@{q^{-n},x^{-1}}{0}{q}{\frac{qx}{a}}.}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle U^{(n)}_{\alpha}}}}$ : Al-Salam-Carlitz I polynomial : http://drmf.wmflabs.org/wiki/Definition:AlSalamCarlitzI
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : 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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Definition:AlSalamCarlitzII >>