Definition:qHahn

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The LaTeX DLMF and DRMF macro \qHahn represents the -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 Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \qHahnin 1:31"): {\displaystyle {\displaystyle \qHahn{n}@{q^{-x}}{\alpha}{\beta}{N}}}
\qHahn{n}@@{q^{-x}}{\alpha}{\beta}{N} produces Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \qHahnin 1:31"): {\displaystyle {\displaystyle \qHahn{n}@@{q^{-x}}{\alpha}{\beta}{N}}}

These are defined by [1]

Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \qHahnin 2:1"): {\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]

Failed to parse (Conversion error. Server ("cli") reported: "SyntaxError: Illegal TeX function Found \qHahnin 2:1"): {\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

 : -Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:qHahn
 : basic hypergeometric (or -hypergeometric) function : http://dlmf.nist.gov/17.4#E1