DLMF:15.4.E2 (Q4985)

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DLMF:15.4.E2
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    Statements

    Defining formula
    F ⁡ ( 1 2 , 1 ; 3 2 ; z 2 ) = 1 2 ⁢ z ⁢ ln ⁡ ( 1 + z 1 - z ) , Gauss-hypergeometric-F 1 2 1 3 2 superscript 𝑧 2 1 2 𝑧 1 𝑧 1 𝑧 {\displaystyle{\displaystyle F\left(\tfrac{1}{2},1;\tfrac{3}{2};z^{2}\right)=% \frac{1}{2z}\ln\left(\frac{1+z}{1-z}\right),}}
    0 references
    DLMF id
    DLMF:15.4.E2
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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.m2aadec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
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    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1adec
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