DLMF:15.4.E13 (Q4997)

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DLMF:15.4.E13
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    test
    F ⁡ ( a , 1 - a ; 1 2 ; - z 2 ) = 1 2 ⁢ 1 + z 2 ⁢ ( ( 1 + z 2 + z ) 2 ⁢ a - 1 + ( 1 + z 2 - z ) 2 ⁢ a - 1 ) , Gauss-hypergeometric-F 𝑎 1 𝑎 1 2 superscript 𝑧 2 1 2 1 superscript 𝑧 2 superscript 1 superscript 𝑧 2 𝑧 2 𝑎 1 superscript 1 superscript 𝑧 2 𝑧 2 𝑎 1 {\displaystyle{\displaystyle F\left(a,1-a;\tfrac{1}{2};-z^{2}\right)=\frac{1}{% 2\sqrt{1+z^{2}}}\left(\left(\sqrt{1+z^{2}}+z\right)^{2a-1}+\left(\sqrt{1+z^{2}% }-z\right)^{2a-1}\right),}}
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    DLMF id
    DLMF:15.4.E13
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