Definition:bigqLegendre

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The LaTeX DLMF and DRMF macro \bigqLegendre represents the big ${\displaystyle{\displaystyle q}}$-Legendre polynomial.

This macro is in the category of polynomials.

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

\bigqLegendre{n} produces ${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$

\bigqLegendre{n}@{x}{c}{q} produces ${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(x;c;q\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(x;c;q\right):=\qHyperrphis{3}{2}@@{q^{-n},q^{n+1},x}{q,cq}{q}{q}.}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : big ${\displaystyle{\displaystyle{\displaystyle q}}}$-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:bigqLegendre
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

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