DLMF:15.8.E20 (Q5077)

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DLMF:15.8.E20
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    Statements

    Defining formula
    F ⁡ ( a , 1 - a c ; z ) = ( 1 - z ) c - 1 ⁢ F ⁡ ( 1 2 ⁢ ( c - a ) , 1 2 ⁢ ( a + c - 1 ) c ; 4 ⁢ z ⁢ ( 1 - z ) ) , Gauss-hypergeometric-F 𝑎 1 𝑎 𝑐 𝑧 superscript 1 𝑧 𝑐 1 Gauss-hypergeometric-F 1 2 𝑐 𝑎 1 2 𝑎 𝑐 1 𝑐 4 𝑧 1 𝑧 {\displaystyle{\displaystyle F\left({a,1-a\atop c};z\right)=(1-z)^{c-1}F\left(% {\frac{1}{2}(c-a),\frac{1}{2}(a+c-1)\atop c};4z(1-z)\right),}}
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    DLMF id
    DLMF:15.8.E20
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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.m2aidec
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