DLMF:15.5.E11 (Q5028)

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DLMF:15.5.E11
No description defined

    Statements

    Defining formula
    ( c - a ) ⁢ F ⁡ ( a - 1 , b ; c ; z ) + ( 2 ⁢ a - c + ( b - a ) ⁢ z ) ⁢ F ⁡ ( a , b ; c ; z ) + a ⁢ ( z - 1 ) ⁢ F ⁡ ( a + 1 , b ; c ; z ) = 0 , 𝑐 𝑎 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 2 𝑎 𝑐 𝑏 𝑎 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑎 𝑧 1 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 0 {\displaystyle{\displaystyle(c-a)F\left(a-1,b;c;z\right)+\left(2a-c+(b-a)z% \right)F\left(a,b;c;z\right)+a(z-1)F\left(a+1,b;c;z\right)=0,}}
    0 references
    DLMF id
    DLMF:15.5.E11
    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.m2aidec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1jdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1idec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1idec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1idec
    0 references
     
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