DLMF:15.9.E8 (Q5098): Difference between revisions

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Property / constraint
 

n = 0 , 1 , 2 , … , N 𝑛 0 1 2 … 𝑁 {\displaystyle{\displaystyle n=0,1,2,\dots,N}}

n=0,1,2,\dots,N
Property / constraint: n = 0 , 1 , 2 , … , N 𝑛 0 1 2 … 𝑁 {\displaystyle{\displaystyle n=0,1,2,\dots,N}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / rank
 
Normal rank
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
 
test:

F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}

\hyperF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
 
xml-id: C15.S2.E1.m2agdec
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
Property / Symbols used
 
Property / Symbols used: Q11649 / rank
 
Normal rank
Property / Symbols used: Q11649 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11649 / qualifier
 
xml-id: C15.S1.XMD1.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11650 / rank
 
Normal rank
Property / Symbols used: Q11650 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11650 / qualifier
 
xml-id: C15.S1.XMD10.m1gdec

Latest revision as of 13:09, 2 January 2020

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DLMF:15.9.E8
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    Statements

    test
    K n ⁡ ( x ; p , N ) = F ⁡ ( - n , - x - N ; 1 p ) , Krawtchouk-polynomial-K 𝑛 𝑥 𝑝 𝑁 Gauss-hypergeometric-F 𝑛 𝑥 𝑁 1 𝑝 {\displaystyle{\displaystyle K_{n}\left(x;p,N\right)=F\left({-n,-x\atop-N};% \frac{1}{p}\right),}}
    0 references
    DLMF id
    DLMF:15.9.E8
    0 references
    constraint
    n = 0 , 1 , 2 , … , N 𝑛 0 1 2 … 𝑁 {\displaystyle{\displaystyle n=0,1,2,\dots,N}}
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    test
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2agdec
    0 references
    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
    Q11649
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C15.S1.XMD1.m1fdec
    0 references
    Q11650
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C15.S1.XMD10.m1gdec
    0 references
     
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