Definition:qHahn

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

This macro is in the category of polynomials.

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

\qHahn{n}@{q^{-x}}{\alpha}{\beta}{N} produces ${\displaystyle{\displaystyle{\displaystyle Q_{n}\!\left(q^{-x};\alpha,\beta,N;\right)}}}$

\qHahn{n}@@{q^{-x}}{\alpha}{\beta}{N} produces ${\displaystyle{\displaystyle{\displaystyle}{Q_{n}\!\left(q^{-x}\right)}}}$

These are defined by

$$Q_{N}\!\left(q^{-x};\alpha,\beta,N;q\right)=\sum_{k=0}^{N}\frac{\left(\alpha\beta q^{N+1};q\right)_{k}\left(q^{-x};q\right)_{k}}{\left(\alpha q;q\right)_{k}\left(q;q\right)_{k}}q^{k}$$

or

${\displaystyle{\displaystyle{\displaystyle Q_{n}\!\left(q^{-x};\alpha,\beta,N;q\right):=\qHyperrphis{3}{2}@@{q^{-n},\alpha\beta q^{n+1},q^{-x}}{\alpha q,q^{-N}}{q}{q}}}}$

Symbols List

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

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