Definition:monicbigqLegendre

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The LaTeX DLMF and DRMF macro \monicbigqLegendre represents the monic big ${\displaystyle{\displaystyle q}}$ polynomial.

This macro is in the category of polynomials.

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

\monicbigqLegendre{n} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}_{n}}}}$

\monicbigqLegendre{n}@{x}{c}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}_{n}\!\left(x;c;q\right)}}}$

\monicbigqLegendre{n}@@{x}{c}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}_{n}\!\left(x;c;q\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(x;c;q\right)=:\frac{\left(q^{n+1};q\right)_{n}}{\left(q,cq;q\right)_{n}}{\widehat{P}}_{n}\!\left(x;c;q\right).}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{P}}_{n}}}}$ : monic big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:monicbigqLegendre
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqLegendre
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

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