Definition:ctsqLegendre

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The LaTeX DLMF and DRMF macro \ctsqLegendre represents the 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:

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

\ctsqLegendre{n}@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(x|q\right)}}}$

\ctsqLegendre{n}@@{x}{q} produces ${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(x|q\right)}}}$

These are defined by

${\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(\lambda(x);c,N|q\right):=\qHyperrphis{3}{2}@@{q^{-n},q^{-x},cq^{x-N}}{q^{-N},0}{q}{q}}.}}$

Symbols List

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

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