Formula:KLS:14.15:01

<< Quantum q-Krawtchouk

formula in q-Krawtchouk

Formula:KLS:14.15:02 >>

${\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(q^{-x};p,N;q\right)=\qHyperrphis{3}{2}@@{q^{-n},q^{-x},-pq^{n}}{q^{-N},0}{q}{q}}}}$

Proof

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Symbols List

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

Bibliography

Equation in Section 14.15 of KLS.

URL links

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<< Quantum q-Krawtchouk

formula in q-Krawtchouk

Formula:KLS:14.15:02 >>