Definition:monicdualqKrawtchouk

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

This macro is in the category of polynomials.

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

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

\monicdualqKrawtchouk{n}@{\lambda(x)}{c}{N}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{K}}_{n}\!\left(\lambda(x);c,N|q\right)}}}$

\monicdualqKrawtchouk{n}@@{\lambda(x)}{c}{N}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{K}}_{n}\!\left(\lambda(x)\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(\lambda(x);c,N|q\right)=:\frac{1}{\left(q^{-N};q\right)_{n}}{\widehat{K}}_{n}\!\left(\lambda(x\right)).}}}$

Symbols List

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

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