DLMF:15.4.E5 (Q4988)

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DLMF:15.4.E5
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    Statements

    Defining formula
    F ⁡ ( 1 2 , 1 2 ; 3 2 ; - z 2 ) = z - 1 ⁢ ln ⁡ ( z + 1 + z 2 ) . Gauss-hypergeometric-F 1 2 1 2 3 2 superscript 𝑧 2 superscript 𝑧 1 𝑧 1 superscript 𝑧 2 {\displaystyle{\displaystyle F\left(\tfrac{1}{2},\tfrac{1}{2};\tfrac{3}{2};-z^% {2}\right)=z^{-1}\ln\left(z+\sqrt{1+z^{2}}\right).}}
    0 references
    DLMF id
    DLMF:15.4.E5
    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.m2addec
    0 references
     
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