Definition:monicctsqLaguerre

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The LaTeX DLMF and DRMF macro \monicctsqLaguerre represents the monic 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:

\monicctsqLaguerre{n} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}^{(n)}_{}}}}$

\monicctsqLaguerre{n}@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}^{(n)}_{@}{x}{q}}}}$

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

These are defined by ${\displaystyle{\displaystyle{\displaystyle P^{(\alpha)}_{n}\!\left(x|q\right)=:\frac{2^{n}q^{(\frac{1}{2}\alpha+\frac{1}{4})n}}{\left(q;q\right)_{n}}{\widehat{P}}^{(\alpha)}_{n}\!\left(x\right).}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}^{(\alpha)}_{n}}}}$ : monic continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:monicctsqLaguerre
${\displaystyle{\displaystyle{\displaystyle P^{(n)}_{\alpha}}}}$ : 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

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