# Definition:AffqKrawtchouk

The LaTeX DLMF and DRMF macro \AffqKrawtchouk represents the Affine ${\displaystyle q}$-Krawtchouk polynomial.

This macro is in the category of polynomials.

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

\AffqKrawtchouk{n} produces $\displaystyle {\displaystyle \AffqKrawtchouk{n}}$
\AffqKrawtchouk{n}@{q^{-x}}{p}{N}{q} produces $\displaystyle {\displaystyle \AffqKrawtchouk{n}@{q^{-x}}{p}{N}{q}}$
\AffqKrawtchouk{n}@@{q^{-x}}{p}{N}{q} produces $\displaystyle {\displaystyle \AffqKrawtchouk{n}@@{q^{-x}}{p}{N}{q}}$

These are defined by $\displaystyle {\displaystyle \AffqKrawtchouk{n}@{q^{-x}}{p}{N}{q}:=\qHyperrphis{3}{2}@@{q^{-n},0,q^{-x}}{pq,q^{-N}}{q}{q} }$

## Symbols List

${\displaystyle {\displaystyle K_{n}^{\mathrm {Aff} }}}$ : affine ${\displaystyle {\displaystyle q}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:AffqKrawtchouk
${\displaystyle {\displaystyle {{}_{r}\phi _{s}}}}$ : basic hypergeometric (or ${\displaystyle {\displaystyle q}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1