Definition:dualqKrawtchouk

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The LaTeX DLMF and DRMF macro \dualqKrawtchouk represents the dual ${\displaystyle{\displaystyle q}}$-Krawtchouk.

This macro is in the category of polynomials.

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

\dualqKrawtchouk{n} produces ${\displaystyle{\displaystyle{\displaystyle K_{n}}}}$

\dualqKrawtchouk{n}@{\lambda(x)}{c}{N}{q} produces ${\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(\lambda(x);c,N|q\right)}}}$

\dualqKrawtchouk{n}@@{\lambda(x)}{c}{N}{q} produces ${\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(\lambda(x)\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(\lambda(x);c,N|q\right):=\qHyperrphis{3}{2}@@{q^{-n},q^{-x},cq^{x-N}}{q^{-N},0}{q}{q}}}}$

Symbols List

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

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