# Definition:dualqKrawtchouk

The LaTeX DLMF and DRMF macro **\dualqKrawtchouk** represents the dual **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}**
-Krawtchouk.

This macro is in the category of polynomials.

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

**\dualqKrawtchouk{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 \dualqKrawtchouk{n}}}****\dualqKrawtchouk{n}@{\lambda(x)}{c}{N}{q}**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 \dualqKrawtchouk{n}@{\lambda(x)}{c}{N}{q}}}****\dualqKrawtchouk{n}@@{\lambda(x)}{c}{N}{q}**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 \dualqKrawtchouk{n}@@{\lambda(x)}{c}{N}{q}}}**

These are defined by
**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 \dualqKrawtchouk{n}@{\lambda(x)}{c}{N}{q}:=\qHyperrphis{3}{2}@@{q^{-n},q^{-x},cq^{x-N}}{q^{-N},0}{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 K_{n}}}**
: dual **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}}**
-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:dualqKrawtchouk

**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