DLMF:15.4.E11 (Q4995)

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DLMF:15.4.E11
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    Statements

    Defining formula
    F ⁡ ( - a , a ; 1 2 ; - z 2 ) = 1 2 ⁢ ( ( 1 + z 2 + z ) 2 ⁢ a + ( 1 + z 2 - z ) 2 ⁢ a ) , Gauss-hypergeometric-F 𝑎 𝑎 1 2 superscript 𝑧 2 1 2 superscript 1 superscript 𝑧 2 𝑧 2 𝑎 superscript 1 superscript 𝑧 2 𝑧 2 𝑎 {\displaystyle{\displaystyle F\left(-a,a;\tfrac{1}{2};-z^{2}\right)=\tfrac{1}{% 2}\left(\left(\sqrt{1+z^{2}}+z\right)^{2a}+\left(\sqrt{1+z^{2}}-z\right)^{2a}% \right),}}
    0 references
    DLMF id
    DLMF:15.4.E11
    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.m2ajdec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1jdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1edec
    0 references
     
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