Formula:KLS:14.15:10

<< Formula:KLS:14.15:09

formula in q-Krawtchouk

Formula:KLS:14.15:12 >>

${\displaystyle{\displaystyle{\displaystyle q^{-n}(1-q^{n})(1+pq^{n})y(x){}=(1-q^{x-N})y(x+1)-\left[(1-q^{x-N})-p(1-q^{x})\right]y(x){}-p(1-q^{x})y(x-1)}}}$

Substitution(s)

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

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:14.15:09

formula in q-Krawtchouk

Formula:KLS:14.15:12 >>