Definition:moniclittleqLegendre

<< Definition:moniclittleqLaguerre

Main Page

Definition:monicMeixner >>

The LaTeX DLMF and DRMF macro \moniclittleqLegendre represents the monic little ${\displaystyle{\displaystyle q}}$ Legendre polynomial.

This macro is in the category of polynomials.

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

\moniclittleqLegendre{n} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{p}}_{n}}}}$

\moniclittleqLegendre{n}@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{p}}_{n}\!\left(x|q\right)}}}$

\moniclittleqLegendre{n}@@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{p}}_{n}\!\left(x\right)}}}$

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

Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{p}}_{n}}}}$ : monic little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:moniclittleqLegendre
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqLegendre
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

<< Definition:moniclittleqLaguerre

Main Page

Definition:monicMeixner >>