DLMF:15.8.E23 (Q5080)

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DLMF:15.8.E23
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    Statements

    Defining formula
    F ⁡ ( a , 1 - a c ; z ) = ( 1 - z - 1 - 1 ) 1 - a ⁢ ( 1 - z - 1 + 1 ) a - 2 ⁢ c + 1 ⁢ ( 1 - z - 1 ) c - 1 ⁢ F ⁡ ( c - a , c - 1 2 2 ⁢ c - 1 ; 4 ⁢ 1 - z - 1 ( 1 - z - 1 + 1 ) 2 ) , Gauss-hypergeometric-F 𝑎 1 𝑎 𝑐 𝑧 superscript 1 superscript 𝑧 1 1 1 𝑎 superscript 1 superscript 𝑧 1 1 𝑎 2 𝑐 1 superscript 1 superscript 𝑧 1 𝑐 1 Gauss-hypergeometric-F 𝑐 𝑎 𝑐 1 2 2 𝑐 1 4 1 superscript 𝑧 1 superscript 1 superscript 𝑧 1 1 2 {\displaystyle{\displaystyle F\left({a,1-a\atop c};z\right)=\left(\sqrt{1-z^{-% 1}}-1\right)^{1-a}\left(\sqrt{1-z^{-1}}+1\right)^{a-2c+1}\left(1-z^{-1}\right)% ^{c-1}F\left({c-a,c-\tfrac{1}{2}\atop 2c-1};\frac{4\sqrt{1-z^{-1}}}{\left(% \sqrt{1-z^{-1}}+1\right)^{2}}\right),}}
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    DLMF id
    DLMF:15.8.E23
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    constraint
    | ph ⁡ ( - z ) | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|<\pi}}
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