Definition:monicqMeixner

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

This macro is in the category of polynomials.

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

\monicqMeixner{n} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{M}}_{n}}}}$

\monicqMeixner{n}@{q^{-x}}{b}{c}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{M}}_{n}\!\left(q^{-x};b,c;q\right)}}}$

\monicqMeixner{n}@@{q^{-x}}{b}{c}{q} produces ${\displaystyle{\displaystyle{\displaystyle{\widehat{M}}_{n}\!\left(q^{-x}\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle M_{n}\!\left(q^{-x};b,c;q\right)=:\frac{(-1)^{n}q^{n^{2}}}{\left(bq;q\right)_{n}c^{n}}{\widehat{M}}_{n}\!\left(q^{-x}\right).}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{M}}_{n}}}}$ : monic ${\displaystyle{\displaystyle{\displaystyle q}}}$-Meixner polynomial : http://drmf.wmflabs.org/wiki/Definition:monicqMeixner
${\displaystyle{\displaystyle{\displaystyle M_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Meixner polynomial : http://drmf.wmflabs.org/wiki/Definition:qMeixner
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

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