DLMF:15.8.E19 (Q5076)

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DLMF:15.8.E19
No description defined

    Statements

    Defining formula
    F ⁡ ( a , 1 - a c ; z ) = ( 1 - 2 ⁢ z ) 1 - a - c ⁢ ( 1 - z ) c - 1 ⁢ F ⁡ ( 1 2 ⁢ ( a + c ) , 1 2 ⁢ ( a + c - 1 ) c ; 4 ⁢ z ⁢ ( z - 1 ) ( 1 - 2 ⁢ z ) 2 ) , Gauss-hypergeometric-F 𝑎 1 𝑎 𝑐 𝑧 superscript 1 2 𝑧 1 𝑎 𝑐 superscript 1 𝑧 𝑐 1 Gauss-hypergeometric-F 1 2 𝑎 𝑐 1 2 𝑎 𝑐 1 𝑐 4 𝑧 𝑧 1 superscript 1 2 𝑧 2 {\displaystyle{\displaystyle F\left({a,1-a\atop c};z\right)=(1-2z)^{1-a-c}(1-z% )^{c-1}F\left({\frac{1}{2}(a+c),\frac{1}{2}(a+c-1)\atop c};\frac{4z(z-1)}{(1-2% z)^{2}}\right),}}
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    DLMF id
    DLMF:15.8.E19
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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.m2ahdec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1acdec
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    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1rdec
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    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1qdec
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    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1jdec
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