Formula:KLS:14.17:08

<< Formula:KLS:14.17:07

formula in Dual q-Krawtchouk

Formula:KLS:14.17:09 >>

${\displaystyle{\displaystyle{\displaystyle x{\widehat{K}}_{n}\!\left(x\right)={\widehat{K}}_{n+1}\!\left(x\right)+(1+c)q^{n-N}{\widehat{K}}_{n}\!\left(x\right){}+cq^{-N}(1-q^{n})(1-q^{n-N-1}){\widehat{K}}_{n-1}\!\left(x\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle{\widehat{K}}_{n}}}}$ : monic dual ${\displaystyle{\displaystyle{\displaystyle q}}}$-Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:monicdualqKrawtchouk

Bibliography

Equation in Section 14.17 of KLS.

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<< Formula:KLS:14.17:07

formula in Dual q-Krawtchouk

Formula:KLS:14.17:09 >>