Definition:ctsqHahn

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The LaTeX DLMF and DRMF macro \ctsqHahn represents the continuous ${\displaystyle{\displaystyle q}}$-Hahn polynomial.

This macro is in the category of polynomials.

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

\ctsqHahn{n} produces ${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$

\ctsqHahn{n}@{x}{a}{b}{c}{d}{q} produces ${\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x;a,b,c,d;q\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle\frac{(a{\mathrm{e}^{i\phi}})^{n}p_{n}\!\left(x;a,b,c,d;q\right)}{\left(ab{\mathrm{e}^{2i\phi}},ac,ad;q\right)_{n}}{}:=\qHyperrphis{4}{3}@@{q^{-n},abcdq^{n-1},a{\mathrm{e}^{i(\theta+2\phi)}},a{\mathrm{e}^{-i\theta}}}{ab{\mathrm{e}^{2i\phi}},ac,ad}{q}{q}.}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle p_{n}}}}$ : continuous ${\displaystyle{\displaystyle{\displaystyle q}}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:ctsqHahn
${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : 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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