DLMF:16.6.E1 (Q5216)

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DLMF:16.6.E1
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    F 2 3 ⁡ ( a , b , c a - b + 1 , a - c + 1 ; z ) = ( 1 - z ) - a ⁢ F 2 3 ⁡ ( a - b - c + 1 , 1 2 ⁢ a , 1 2 ⁢ ( a + 1 ) a - b + 1 , a - c + 1 ; - 4 ⁢ z ( 1 - z ) 2 ) . Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑎 𝑏 1 𝑎 𝑐 1 𝑧 superscript 1 𝑧 𝑎 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 1 1 2 𝑎 1 2 𝑎 1 𝑎 𝑏 1 𝑎 𝑐 1 4 𝑧 superscript 1 𝑧 2 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,b,c\atop a-b+1,a-c+1};z% \right)=(1-z)^{-a}{{}_{3}F_{2}}\left({a-b-c+1,\frac{1}{2}a,\frac{1}{2}(a+1)% \atop a-b+1,a-c+1};\frac{-4z}{(1-z)^{2}}\right).}}
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    DLMF id
    DLMF:16.6.E1
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