DLMF:15.4.E17 (Q5001)

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DLMF:15.4.E17
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    Statements

    Defining formula
    F ⁡ ( a , 1 2 + a ; 1 + 2 ⁢ a ; z ) = ( 1 2 + 1 2 ⁢ 1 - z ) - 2 ⁢ a , Gauss-hypergeometric-F 𝑎 1 2 𝑎 1 2 𝑎 𝑧 superscript 1 2 1 2 1 𝑧 2 𝑎 {\displaystyle{\displaystyle F\left(a,\tfrac{1}{2}+a;1+2a;z\right)=\left(% \tfrac{1}{2}+\tfrac{1}{2}\sqrt{1-z}\right)^{-2a},}}
    0 references
    DLMF id
    DLMF:15.4.E17
    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.m2apdec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1pdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1kdec
    0 references
     
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