DLMF:15.8.E16 (Q5073)

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DLMF:15.8.E16
No description defined

    Statements

    Defining formula
    F ⁡ ( a , b a - b + 1 ; z ) = ( 1 - z ) - a ⁢ F ⁡ ( 1 2 ⁢ a , 1 2 ⁢ a - b + 1 2 a - b + 1 ; - 4 ⁢ z ( 1 - z ) 2 ) , Gauss-hypergeometric-F 𝑎 𝑏 𝑎 𝑏 1 𝑧 superscript 1 𝑧 𝑎 Gauss-hypergeometric-F 1 2 𝑎 1 2 𝑎 𝑏 1 2 𝑎 𝑏 1 4 𝑧 superscript 1 𝑧 2 {\displaystyle{\displaystyle F\left({a,b\atop a-b+1};z\right)=(1-z)^{-a}F\left% ({\frac{1}{2}a,\frac{1}{2}a-b+\frac{1}{2}\atop a-b+1};\frac{-4z}{(1-z)^{2}}% \right),}}
    0 references
    DLMF id
    DLMF:15.8.E16
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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    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.m2aedec
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    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1odec
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    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1ndec
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    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1ndec
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