Formula:KLS:14.15:12

<< Formula:KLS:14.15:10

formula in q-Krawtchouk

Formula:KLS:14.15:13 >>

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

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:14.15:10

formula in q-Krawtchouk

Formula:KLS:14.15:13 >>