Definition:moniclittleqJacobi

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The LaTeX DLMF and DRMF macro \moniclittleqJacobi represents the monic little q Jacobi polynomial.

This macro is in the category of polynomials.

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

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

\moniclittleqJacobi{n}@{x}{a}{b}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{p}}_{n}\!\left(x;a,b;q\right)}}}$

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

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

Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{p}}_{n}}}}$ : monic little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:moniclittleqJacobi
${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : little ${\displaystyle{\displaystyle{\displaystyle q}}}$-Jacobi polynomial : http://drmf.wmflabs.org/wiki/Definition:littleqJacobi
${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : 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

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