DLMF:15.4.E15 (Q4999)

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DLMF:15.4.E15
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    Statements

    Defining formula
    F ⁡ ( a , 1 - a ; 3 2 ; - z 2 ) = 1 ( 2 - 4 ⁢ a ) ⁢ z ⁢ ( ( 1 + z 2 + z ) 1 - 2 ⁢ a - ( 1 + z 2 - z ) 1 - 2 ⁢ a ) , Gauss-hypergeometric-F 𝑎 1 𝑎 3 2 superscript 𝑧 2 1 2 4 𝑎 𝑧 superscript 1 superscript 𝑧 2 𝑧 1 2 𝑎 superscript 1 superscript 𝑧 2 𝑧 1 2 𝑎 {\displaystyle{\displaystyle F\left(a,1-a;\tfrac{3}{2};-z^{2}\right)=\frac{1}{% (2-4a)z}\left(\left(\sqrt{1+z^{2}}+z\right)^{1-2a}-\left(\sqrt{1+z^{2}}-z% \right)^{1-2a}\right),}}
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    DLMF id
    DLMF:15.4.E15
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