Definition:monicqKrawtchouk

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

This macro is in the category of polynomials.

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

\monicqKrawtchouk{n} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{K}}_{n}}}}$

\monicqKrawtchouk{n}@{q^{-x}}{p}{N}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{K}}_{n}\!\left(q^{-x};p,N;q\right)}}}$

\monicqKrawtchouk{n}@@{q^{-x}}{p}{N}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{K}}_{n}\!\left(q^{-x}\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(q^{-x};p,N;q\right)=:\frac{\left(-pq^{n};q\right)_{n}}{\left(q^{-N};q\right)_{n}}{\widehat{K}}_{n}\!\left(q^{-x}\right).}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{K}}_{n}}}}$ : monic ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:monicqKrawtchouk
${\displaystyle{\displaystyle{\displaystyle K_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:qKrawtchouk
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

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