DLMF:15.5.E13 (Q5030)

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DLMF:15.5.E13
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    ( c - a - b ) F ( a , b ; c ; z ) + a ( 1 - z ) F ( a + 1 , b ; c ; z ) - ( c - b ) F ( a , b - 1 ; c ; z ) = 0 , 𝑐 𝑎 𝑏 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑎 1 𝑧 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 𝑐 𝑏 Gauss-hypergeometric-F 𝑎 𝑏 1 𝑐 𝑧 0 {\displaystyle{\displaystyle(c-a-b)F\left(a,b;c;z\right)+a(1-z)F\left(a+1,b;c;% z\right)-(c-b)F\left(a,b-1;c;z\right)=0,}}
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