Formula:KLS:14.15:14

<< Formula:KLS:14.15:13

formula in q-Krawtchouk

Formula:KLS:14.15:15 >>

${\displaystyle{\displaystyle{\displaystyle(1-q^{x-N-1})K_{n}\!\left(q^{-x};p,N;q\right)+pq^{-1}(1-q^{x})K_{n}\!\left(q^{-x+1};p,N;q\right){}=q^{x}(1-q^{-N-1})K_{n+1}\!\left(q^{-x};pq^{-2},N+1;q\right)}}}$

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

Bibliography

Equation in Section 14.15 of KLS.

URL links

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<< Formula:KLS:14.15:13

formula in q-Krawtchouk

Formula:KLS:14.15:15 >>