DLMF:15.4.E3 (Q4986)

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DLMF:15.4.E3
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    Statements

    Defining formula
    F ⁡ ( 1 2 , 1 ; 3 2 ; - z 2 ) = z - 1 ⁢ arctan ⁡ z , Gauss-hypergeometric-F 1 2 1 3 2 superscript 𝑧 2 superscript 𝑧 1 𝑧 {\displaystyle{\displaystyle F\left(\tfrac{1}{2},1;\tfrac{3}{2};-z^{2}\right)=% z^{-1}\operatorname{arctan}z,}}
    0 references
    DLMF id
    DLMF:15.4.E3
    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.m2abdec
    0 references
     
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