Formula:KLS:14.15:13

<< Formula:KLS:14.15:12

formula in q-Krawtchouk

Formula:KLS:14.15:14 >>

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

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:14.15:12

formula in q-Krawtchouk

Formula:KLS:14.15:14 >>