# Definition:qHahn

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

This macro is in the category of polynomials.

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

\qHahn{n}@{q^{-x}}{\alpha}{\beta}{N} produces $\displaystyle {\displaystyle \qHahn{n}@{q^{-x}}{\alpha}{\beta}{N}}$
\qHahn{n}@@{q^{-x}}{\alpha}{\beta}{N} produces $\displaystyle {\displaystyle \qHahn{n}@@{q^{-x}}{\alpha}{\beta}{N}}$

These are defined by [1]

$\displaystyle \qHahn{N}@{q^{-x}}{\alpha}{\beta}{N}{q}=\sum_{k=0}^N \frac{\qPochhammer{\alpha\beta q^{N+1}}{q}{k}\qPochhammer{q^{-x}}{q}{k}}{\qPochhammer{\alpha q}{q}{k}\qPochhammer{q}{q}{k}}q^k$

or [2]

$\displaystyle {\displaystyle \qHahn{n}@{q^{-x}}{\alpha}{\beta}{N}{q}:=\qHyperrphis{3}{2}@@{q^{-n},\alpha\beta q^{n+1},q^{-x}}{\alpha q,q^{-N}}{q}{q} }$

## Symbols List

${\displaystyle {\displaystyle Q_{n}}}$ : ${\displaystyle {\displaystyle q}}$-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:qHahn
${\displaystyle {\displaystyle {{}_{r}\phi _{s}}}}$ : basic hypergeometric (or ${\displaystyle {\displaystyle q}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1