DLMF:15.8.E16 (Q5073)

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DLMF:15.8.E16
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    test
    F ⁡ ( a , b a - b + 1 ; z ) = ( 1 - z ) - a ⁢ F ⁡ ( 1 2 ⁢ a , 1 2 ⁢ a - b + 1 2 a - b + 1 ; - 4 ⁢ z ( 1 - z ) 2 ) , Gauss-hypergeometric-F 𝑎 𝑏 𝑎 𝑏 1 𝑧 superscript 1 𝑧 𝑎 Gauss-hypergeometric-F 1 2 𝑎 1 2 𝑎 𝑏 1 2 𝑎 𝑏 1 4 𝑧 superscript 1 𝑧 2 {\displaystyle{\displaystyle F\left({a,b\atop a-b+1};z\right)=(1-z)^{-a}F\left% ({\frac{1}{2}a,\frac{1}{2}a-b+\frac{1}{2}\atop a-b+1};\frac{-4z}{(1-z)^{2}}% \right),}}
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    DLMF id
    DLMF:15.8.E16
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