DLMF:18.23.E3 (Q5904): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11662 / rank
 
Normal rank
Property / Symbols used: Q11662 / qualifier
 
test:

K n ⁡ ( x ; p , N ) Krawtchouk-polynomial-K 𝑛 𝑥 𝑝 𝑁 {\displaystyle{\displaystyle K_{\NVar{n}}\left(\NVar{x};\NVar{p},\NVar{N}% \right)}}

\KrawtchoukpolyK{\NVar{n}}@{\NVar{x}}{\NVar{p}}{\NVar{N}}
Property / Symbols used: Q11662 / qualifier
 
xml-id: C18.S19.T1.t1.r3.p1.m2adec

Revision as of 00:39, 2 January 2020

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DLMF:18.23.E3
No description defined

    Statements

    test
    ( 1 - 1 - p p ⁢ z ) x ⁢ ( 1 + z ) N - x = ∑ n = 0 N ( N n ) ⁢ K n ⁡ ( x ; p , N ) ⁢ z n , superscript 1 1 𝑝 𝑝 𝑧 𝑥 superscript 1 𝑧 𝑁 𝑥 superscript subscript 𝑛 0 𝑁 binomial 𝑁 𝑛 Krawtchouk-polynomial-K 𝑛 𝑥 𝑝 𝑁 superscript 𝑧 𝑛 {\displaystyle{\displaystyle\left(1-\frac{1-p}{p}z\right)^{x}(1+z)^{N-x}=\sum_% {n=0}^{N}\genfrac{(}{)}{0.0pt}{}{N}{n}K_{n}\left(x;p,N\right)z^{n},}}
    0 references
    DLMF id
    DLMF:18.23.E3
    0 references
    constraint
    x = 0 , 1 , … , N 𝑥 0 1 … 𝑁 {\displaystyle{\displaystyle x=0,1,\dots,N}}
    0 references
    Symbols used
    Q11662
    test
    K n ⁡ ( x ; p , N ) Krawtchouk-polynomial-K 𝑛 𝑥 𝑝 𝑁 {\displaystyle{\displaystyle K_{\NVar{n}}\left(\NVar{x};\NVar{p},\NVar{N}% \right)}}
    xml-id
    C18.S19.T1.t1.r3.p1.m2adec
    0 references
     
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