DLMF:15.8.E14 (Q5071)

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DLMF:15.8.E14
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    Statements

    test
    F ⁡ ( a , b 2 ⁢ b ; z ) = ( 1 - z ) - a / 2 ⁢ F ⁡ ( 1 2 ⁢ a , b - 1 2 ⁢ a b + 1 2 ; z 2 4 ⁢ z - 4 ) , Gauss-hypergeometric-F 𝑎 𝑏 2 𝑏 𝑧 superscript 1 𝑧 𝑎 2 Gauss-hypergeometric-F 1 2 𝑎 𝑏 1 2 𝑎 𝑏 1 2 superscript 𝑧 2 4 𝑧 4 {\displaystyle{\displaystyle F\left({a,b\atop 2b};z\right)=\left(1-z\right)^{-% \ifrac{a}{2}}F\left({\tfrac{1}{2}a,b-\tfrac{1}{2}a\atop b+\tfrac{1}{2}};\frac{% z^{2}}{4z-4}\right),}}
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    DLMF id
    DLMF:15.8.E14
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    constraint
    | ph ⁡ ( 1 - z ) | < π phase 1 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
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