Definition:qMeixnerPollaczek

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The LaTeX DLMF and DRMF macro \qMeixnerPollaczek represents the ${\displaystyle{\displaystyle q}}$-Meixner Pollaczek polynomial.

This macro is in the category of polynomials.

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

\qMeixnerPollaczek{n} produces ${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$

\qMeixnerPollaczek{n}@{x}{a}{q} produces ${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(x;a|q\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle P_{n}\!\left(x;a|q\right):=a^{-n}{\mathrm{e}^{-in\phi}}\frac{\left(a^{2};q\right)_{n}}{\left(q;q\right)_{n}}\,\qHyperrphis{3}{2}@@{q^{-n},a{\mathrm{e}^{i(\theta+2\phi)}},a{\mathrm{e}^{-i\theta}}}{a^{2},0}{q}{q}}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Meixner-Pollaczek polynomial : http://drmf.wmflabs.org/wiki/Definition:qMeixnerPollaczek
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
${\displaystyle{\displaystyle{\displaystyle(a;q)_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

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