# Definition:qtmqKrawtchouk

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

This macro is in the category of polynomials.

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

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

These are defined by $\displaystyle {\displaystyle \qtmqKrawtchouk{n}@{q^{-x}}{p}{N}{q}:= \qHyperrphis{2}{1}@@{q^{-n},q^{-x}}{q^{-N}}{q}{pq^{n+1}} }$

## Symbols List

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