Definition:monicqCharlier

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

This macro is in the category of polynomials.

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

\monicqCharlier{n} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{C}}_{n}}}}$

\monicqCharlier{n}@{q^{-x}}{a}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{C}}_{n}\!\left(q^{-x};a;q\right)}}}$

\monicqCharlier{n}@@{q^{-x}}{a}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{C}}_{n}\!\left(q^{-x}\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle Q_{n}\!\left(q^{-x};\alpha,\beta,N;q\right)=:\frac{\left(\alpha\beta q^{n+1};q\right)_{n}}{\left(\alpha q,q^{-N};q\right)_{n}}{\widehat{Q}}_{n}\!\left(q^{-x}\right).}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{C}}_{n}}}}$ : monic ${\displaystyle{\displaystyle{\displaystyle q}}}$-Charlier polynomial : http://drmf.wmflabs.org/wiki/Definition:monicqCharlier
${\displaystyle{\displaystyle{\displaystyle Q_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:qHahn
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{\widehat{Q}}_{n}}}}$ : monic ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:monicqHahn

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