Definition:qLaguerre

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

This macro is in the category of polynomials.

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

\qLaguerre{n} produces ${\displaystyle{\displaystyle{\displaystyle L_{n}}}}$

\qLaguerre[\alpha]{n} produces ${\displaystyle{\displaystyle{\displaystyle L^{(\alpha)}_{n}}}}$

\qLaguerre{n}@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle L_{n}\!\left(x;q\right)}}}$

\qLaguerre[\alpha]{n}@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle L^{(\alpha)}_{n}\!\left(x;q\right)}}}$

\qLaguerre{n}@@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle L_{n}\!\left(x\right)}}}$

\qLaguerre[\alpha]{n}@@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle L^{(\alpha)}_{n}\!\left(x\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle L^{(\alpha)}_{n}\!\left(x;q\right):=\frac{\left(q^{\alpha+1};q\right)_{n}}{\left(q;q\right)_{n}}\,\qHyperrphis{1}{1}@@{q^{-n}}{q^{\alpha+1}}{q}{-q^{n+\alpha+1}x}}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle L_{n}^{(\alpha)}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Laguerre polynomial : http://drmf.wmflabs.org/wiki/Definition:qLaguerre
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-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

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