Formula:6544

Digital Library of Mathematical Functions ID 18.20.E6

${\displaystyle{\displaystyle K_{n}\left(x;p,N\right)={{}_{2}F_{1}}\left({-n,-x\atop-N};p^{-1}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle n=0,1,\dots,N}}$

Symbols List

• ${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: = F ( a , b ; c ; z ) notation for Gauss’ hypergeometric function
• ${\displaystyle{\displaystyle K_{\NVar{n}}\left(\NVar{x};\NVar{p},\NVar{N}\right)}}$: Krawtchouk polynomial
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle N}}$: positive integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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