Definition:monicAffqKrawtchouk

<< Definition:monicqinvAlSalamChihara

Main Page

Definition:qMeixnerPollaczek >>

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

This macro is in the category of polynomials.

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

\monicAffqKrawtchouk{n} produces ${\displaystyle{\displaystyle{\displaystyle\widehat{K}^{\mathrm{Aff}}_{n}}}}$

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

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

These are defined by ${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{Aff}}_{n}\!\left(q^{-x};p,N;q\right)=:\frac{1}{\left(pq,q^{-N};q\right)_{n}}\widehat{K}^{\mathrm{Aff}}_{n}\!\left(q^{-x};p,N;q\right).}}}$

Symbols List

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

<< Definition:monicqinvAlSalamChihara

Main Page

Definition:qMeixnerPollaczek >>