Formula:KLS:09.11:05

<< Formula:KLS:09.11:04

formula in Krawtchouk

Formula:KLS:09.11:06 >>

${\displaystyle{\displaystyle{\displaystyle K_{n}\!\left(x;p,N\right)=\frac{1}{{\left(-N\right)_{n}}p^{n}}{\widehat{K}}_{n}\!\left(x\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle K_{n}}}}$ : Krawtchouk polynomial : http://dlmf.nist.gov/18.19#T1.t1.r6
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle{\widehat{K}}_{n}}}}$ : monic Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:monicKrawtchouk

Bibliography

Equation in Section 9.11 of KLS.

URL links

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<< Formula:KLS:09.11:04

formula in Krawtchouk

Formula:KLS:09.11:06 >>