Formula:KLS:09.11:01

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formula in Krawtchouk

Formula:KLS:09.11:02 >>

${\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(x;p,N\right)=\HyperpFq{2}{1}@@{-n,-x}{-N}{\frac{1}{p}}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle n=0,1,2,\ldots,N}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle K_{n}}}}$ : Krawtchouk polynomial : http://dlmf.nist.gov/18.19#T1.t1.r6
${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1

Bibliography

Equation in Section 9.11 of KLS.

URL links

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formula in Krawtchouk

Formula:KLS:09.11:02 >>