DLMF:15.5.E16 (Q5033): 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.m2andec

Revision as of 12:55, 2 January 2020

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DLMF:15.5.E16
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    Statements

    test
    c ⁢ ( 1 - z ) ⁢ F ⁡ ( a , b ; c ; z ) - c ⁢ F ⁡ ( a - 1 , b ; c ; z ) + ( c - b ) ⁢ z ⁢ F ⁡ ( a , b ; c + 1 ; z ) = 0 , 𝑐 1 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑐 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 𝑐 𝑏 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 1 𝑧 0 {\displaystyle{\displaystyle c(1-z)F\left(a,b;c;z\right)-cF\left(a-1,b;c;z% \right)+(c-b)zF\left(a,b;c+1;z\right)=0,}}
    0 references
    DLMF id
    DLMF:15.5.E16
    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.m2andec
    0 references
     
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