Definition:ctsqLaguerre

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

This macro is in the category of polynomials.

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

\ctsqLaguerre{\alpha}{n} produces ${\displaystyle{\displaystyle{\displaystyle P^{(\alpha)}_{n}}}}$

\ctsqLaguerre{\alpha}{n}@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle P^{(\alpha)}_{n}\!\left(x|q\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle P^{(\alpha)}_{n}\!\left(x|q\right):=\frac{\left(q^{\alpha+1};q\right)_{n}}{\left(q;q\right)_{n}}\,\qHyperrphis{3}{2}@@{q^{-n},q^{\frac{1}{2}\alpha+\frac{1}{4}}{\mathrm{e}^{i\theta}},q^{\frac{1}{2}\alpha+\frac{1}{4}}{\mathrm{e}^{-i\theta}}}{q^{\alpha+1},0}{q}{q}.}}\)\@add@PDF@RDFa@triples\end{document}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle P^{(n)}_{\alpha}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqLaguerre
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11

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