# Definition:ctsqLegendre

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The LaTeX DLMF and DRMF macro \ctsqLegendre represents the continuous $\displaystyle q$ -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 $\displaystyle {\displaystyle \ctsqLegendre{n}}$
\ctsqLegendre{n}@{x}{q} produces $\displaystyle {\displaystyle \ctsqLegendre{n}@{x}{q}}$
\ctsqLegendre{n}@@{x}{q} produces $\displaystyle {\displaystyle \ctsqLegendre{n}@@{x}{q}}$

These are defined by

$\displaystyle {\displaystyle \dualqKrawtchouk{n}@{\lambda(x)}{c}{N}{q}:=\qHyperrphis{3}{2}@@{q^{-n},q^{-x},cq^{x-N}}{q^{-N},0}{q}{q} }.$

## Symbols List

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