DLMF:15.5.E14 (Q5031)

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DLMF:15.5.E14
No description defined

    Statements

    Defining formula
    c ⁢ ( a + ( b - c ) ⁢ z ) ⁢ F ⁡ ( a , b ; c ; z ) - a ⁢ c ⁢ ( 1 - z ) ⁢ F ⁡ ( a + 1 , b ; c ; z ) + ( c - a ) ⁢ ( c - b ) ⁢ z ⁢ F ⁡ ( a , b ; c + 1 ; z ) = 0 , 𝑐 𝑎 𝑏 𝑐 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑎 𝑐 1 𝑧 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 𝑐 𝑎 𝑐 𝑏 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 1 𝑧 0 {\displaystyle{\displaystyle c\left(a+(b-c)z\right)F\left(a,b;c;z\right)-ac(1-% z)F\left(a+1,b;c;z\right)+(c-a)(c-b)zF\left(a,b;c+1;z\right)=0,}}
    0 references
    DLMF id
    DLMF:15.5.E14
    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.m2aldec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1mdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1ldec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1ldec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1ldec
    0 references
     
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