Definition:qtmqKrawtchouk

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The LaTeX DLMF and DRMF macro \qtmqKrawtchouk represents the quantum ${\displaystyle{\displaystyle q}}$-Krawtchouk polynomial.

This macro is in the category of polynomials.

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

\qtmqKrawtchouk{n} produces ${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{qtm}}_{n}}}}$

\qtmqKrawtchouk{n}@{q^{-x}}{p}{N}{q} produces ${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{qtm}}_{n}\!\left(q^{-x};p,N;q\right)}}}$

\qtmqKrawtchouk{n}@@{q^{-x}}{p}{N}{q} produces ${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{qtm}}_{n}\!\left(q^{-x}\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{qtm}}_{n}\!\left(q^{-x};p,N;q\right):=\qHyperrphis{2}{1}@@{q^{-n},q^{-x}}{q^{-N}}{q}{pq^{n+1}}}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle K^{\mathrm{qtm}}_{n}}}}$ : quantum ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:qtmqKrawtchouk
${\displaystyle{\displaystyle{\displaystyle{{}_{r}\phi_{s}}}}}$ : basic hypergeometric (or ${\displaystyle{\displaystyle{\displaystyle q}}}$-hypergeometric) function : http://dlmf.nist.gov/17.4#E1

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