# Definition:ctsHahn

The LaTeX DLMF and DRMF macro \ctsHahn represents the Continuous Hahn polynomial.

This macro is in the category of polynomials.

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

\ctsHahn{n} produces $\displaystyle {\displaystyle \ctsHahn{n}}$
\ctsHahn{n}@{x}{a}{b}{c}{d} produces $\displaystyle {\displaystyle \ctsHahn{n}@{x}{a}{b}{c}{d}}$
\ctsHahn{n}@@{x}{a}{b}{c}{d} produces $\displaystyle {\displaystyle \ctsHahn{n}@@{x}{a}{b}{c}{d}}$

These are defined by $\displaystyle {\displaystyle \ctsHahn{n}@{x}{a}{b}{c}{d} {}:=i^n\frac{\pochhammer{a+c}{n}\pochhammer{a+d}{n}}{n!}\,\HyperpFq{3}{2}@@{-n,n+a+b+c+d-1,a+ix}{a+c,a+d}{1} }$

## Symbols List

${\displaystyle {\displaystyle p_{n}}}$ : continuous Hahn polynomial : http://dlmf.nist.gov/18.19#P2.p1
${\displaystyle {\displaystyle (a)_{n}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle {\displaystyle {{}_{p}F_{q}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1