Definition:monicctsqLegendre

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

This macro is in the category of polynomials.

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

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

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

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

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

Symbols List

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

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