DLMF:15.8.E17 (Q5074)

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DLMF:15.8.E17
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    Statements

    Defining formula
    F ⁡ ( a , b 1 2 ⁢ ( a + b + 1 ) ; z ) = ( 1 - 2 ⁢ z ) - a ⁢ F ⁡ ( 1 2 ⁢ a , 1 2 ⁢ a + 1 2 1 2 ⁢ ( a + b + 1 ) ; 4 ⁢ z ⁢ ( z - 1 ) ( 1 - 2 ⁢ z ) 2 ) , Gauss-hypergeometric-F 𝑎 𝑏 1 2 𝑎 𝑏 1 𝑧 superscript 1 2 𝑧 𝑎 Gauss-hypergeometric-F 1 2 𝑎 1 2 𝑎 1 2 1 2 𝑎 𝑏 1 4 𝑧 𝑧 1 superscript 1 2 𝑧 2 {\displaystyle{\displaystyle F\left({a,b\atop\frac{1}{2}(a+b+1)};z\right)=(1-2% z)^{-a}F\left({\frac{1}{2}a,\frac{1}{2}a+\frac{1}{2}\atop\frac{1}{2}(a+b+1)};% \frac{4z(z-1)}{(1-2z)^{2}}\right),}}
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    DLMF id
    DLMF:15.8.E17
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    constraint
    ℜ ⁡ z < 1 2 𝑧 1 2 {\displaystyle{\displaystyle\Re z<\frac{1}{2}}}
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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.m2afdec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
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    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1pdec
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    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1odec
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    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1odec
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