Definition:qKrawtchouk

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

This macro is in the category of polynomials.

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

\qKrawtchouk{n} produces ${\displaystyle{\displaystyle{\displaystyle K_{n}}}}$

\qKrawtchouk{n}@{q^{-x}}{p}{N}{q} produces ${\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(q^{-x};p,N;q\right)}}}$

\qKrawtchouk{n}@@{q^{-x}}{p}{N}{q} produces ${\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(q^{-x}\right)}}}$

These are defined by ${\displaystyle{\displaystyle K_{n}\!\left(q^{-x};p,N;q\right):=\qHyperrphis{3}{2}@@{q^{-n},q^{-x},-pq^{n}}{q^{-N},0}{q}{q}.\end{equation}}}$

Symbols List

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

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