Formula:KLS:14.15:27

<< Formula:KLS:14.15:25

formula in q-Krawtchouk

Formula:KLS:14.16:01 >>

${\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(\lambda(x);c,N|q\right)=K_{x}\!\left(q^{-n};-cq^{-N},N;q\right)}}}$

Substitution(s)

${\displaystyle{\displaystyle{\displaystyle\lambda(n)=q^{-n}-pq^{n}}}}$ &
${\displaystyle{\displaystyle{\displaystyle\lambda(x)=q^{-x}+cq^{x-N}}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle K_{n}}}}$ : dual ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:dualqKrawtchouk
${\displaystyle{\displaystyle{\displaystyle K_{n}}}}$ : ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:qKrawtchouk

Bibliography

Equation in Section 14.15 of KLS.

URL links

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<< Formula:KLS:14.15:25

formula in q-Krawtchouk

Formula:KLS:14.16:01 >>