Definition:monicqtmqKrawtchouk

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

This macro is in the category of polynomials.

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

\monicqtmqKrawtchouk{n} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{K}^{\mathrm{qtm}}}_{n}}}}$

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

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

These are defined by ${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{qtm}}_{n}\!\left(q^{-x};p,N;q\right)=:\frac{p^{n}q^{n^{2}}}{\left(q^{-N};q\right)_{n}}{\widehat{K}^{\mathrm{qtm}}}_{n}\!\left(q^{-x}\right).}}}$

Symbols List

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

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