Formula:KLS:09.11:37

<< Formula:KLS:09.11:36

formula in Krawtchouk

Formula:KLS:09.12:01 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \sum_{x=0}^N\binom Nx \Krawtchouk{m}@{x}{p}{N}\Krawtchouk{n}@{x}{q}{N}z^x =\left(\frac{p-z+pz}p\right)^m \left(\frac{q-z+qz}q\right)^n (1+z)^{N-m-n} \Krawtchouk{m}@{n}{- \frac{(p-z+pz)(q-z+qz)}z}{N} }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Sigma}}  : sum : http://drmf.wmflabs.org/wiki/Definition:sum
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \binom{n}{k}}}  : binomial coefficient : http://dlmf.nist.gov/1.2#E1 http://dlmf.nist.gov/26.3#SS1.p1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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 in Krawtchouk

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