# Definition:Hahn

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

This macro is in the category of polynomials.

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

\Hahn{n} produces $\displaystyle {\displaystyle \Hahn{n}}$
\Hahn{n}@{x}{\alpha}{\beta}{N} produces $\displaystyle {\displaystyle \Hahn{n}@{x}{\alpha}{\beta}{N}}$

These are defined by $\displaystyle {\displaystyle \Hahn{n}@{x}{\alpha}{\beta}{N}:=\HyperpFq{3}{2}@@{-n,n+\alpha+\beta+1,-x}{\alpha+1,-N}{1} }$

## Symbols List

${\displaystyle {\displaystyle Q_{n}}}$ : Hahn polynomial : http://dlmf.nist.gov/18.19#T1.t1.r3
${\displaystyle {\displaystyle {{}_{p}F_{q}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1