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

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
Property / constraint
 

x = 0 , 1 , , N 𝑥 0 1 𝑁 {\displaystyle{\displaystyle x=0,1,\dots,N}}

x=0,1,\dots,N
Property / constraint: x = 0 , 1 , , N 𝑥 0 1 𝑁 {\displaystyle{\displaystyle x=0,1,\dots,N}} / rank
 
Normal rank

Revision as of 17:02, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:18.23.E3
No description defined

    Statements

    ( 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
    0 references
    x = 0 , 1 , , N 𝑥 0 1 𝑁 {\displaystyle{\displaystyle x=0,1,\dots,N}}
    0 references