# Definition:qHahn

The LaTeX DLMF and DRMF macro **\qHahn** represents the **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\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**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle \qHahn{n}@{q^{-x}}{\alpha}{\beta}{N}}}****\qHahn{n}@@{q^{-x}}{\alpha}{\beta}{N}**produces**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle \qHahn{n}@@{q^{-x}}{\alpha}{\beta}{N}}}**

These are defined by ^{[1]}

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\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 (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\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

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle Q_{n}}}**
: **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle q}}**
-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:qHahn

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle {{}_{r}\phi_{s}}}}**
: basic hypergeometric (or **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle q}}**
-hypergeometric) function : http://dlmf.nist.gov/17.4#E1