DLMF:15.5.E17 (Q5034): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11647 / rank
 
Normal rank
Property / Symbols used: Q11647 / qualifier
 
Defining formula:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q11647 / qualifier
 
xml-id: C15.S1.XMD6.m1odec

Latest revision as of 13:55, 2 January 2020

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DLMF:15.5.E17
No description defined

    Statements

    Defining formula
    ( a - 1 + ( b + 1 - c ) ⁢ z ) ⁢ F ⁡ ( a , b ; c ; z ) + ( c - a ) ⁢ F ⁡ ( a - 1 , b ; c ; z ) - ( c - 1 ) ⁢ ( 1 - z ) ⁢ F ⁡ ( a , b ; c - 1 ; z ) = 0 , 𝑎 1 𝑏 1 𝑐 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑐 𝑎 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 𝑐 1 1 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 1 𝑧 0 {\displaystyle{\displaystyle\left(a-1+(b+1-c)z\right)F\left(a,b;c;z\right)+(c-% a)F\left(a-1,b;c;z\right)-(c-1)(1-z)F\left(a,b;c-1;z\right)=0,}}
    0 references
    DLMF id
    DLMF:15.5.E17
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    Defining formula
    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.m2aodec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1pdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1odec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1odec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1odec
    0 references
     
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