DLMF:15.5.E13 (Q5030): Difference between revisions

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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.m2akdec

Revision as of 12:54, 2 January 2020

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DLMF:15.5.E13
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    Statements

    test
    ( c - a - b ) ⁢ F ⁡ ( a , b ; c ; z ) + a ⁢ ( 1 - z ) ⁢ F ⁡ ( a + 1 , b ; c ; z ) - ( c - b ) ⁢ F ⁡ ( a , b - 1 ; c ; z ) = 0 , 𝑐 𝑎 𝑏 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑎 1 𝑧 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 𝑐 𝑏 Gauss-hypergeometric-F 𝑎 𝑏 1 𝑐 𝑧 0 {\displaystyle{\displaystyle(c-a-b)F\left(a,b;c;z\right)+a(1-z)F\left(a+1,b;c;% z\right)-(c-b)F\left(a,b-1;c;z\right)=0,}}
    0 references
    DLMF id
    DLMF:15.5.E13
    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.m2akdec
    0 references
     
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