Formula:KLS:09.11:12

<< Formula:KLS:09.11:11

formula in Krawtchouk

Formula:KLS:09.11:13 >>

${\displaystyle{\displaystyle{\displaystyle\binomial{N}{x}\left(\frac{p}{1-p}\right)^{x}K_{n}\!\left(x;p,N\right)=\nabla^{n}\left[\binomial{N-n}{x}\left(\frac{p}{1-p}\right)^{x}\right]}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{n}{k}}}}$ : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
${\displaystyle{\displaystyle{\displaystyle K_{n}}}}$ : Krawtchouk polynomial : http://dlmf.nist.gov/18.19#T1.t1.r6

Bibliography

Equation in Section 9.11 of KLS.

URL links

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<< Formula:KLS:09.11:11

formula in Krawtchouk

Formula:KLS:09.11:13 >>