DLMF:15.5.E16 (Q5033)

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DLMF:15.5.E16
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    c ( 1 - z ) F ( a , b ; c ; z ) - c F ( a - 1 , b ; c ; z ) + ( c - b ) z F ( a , b ; c + 1 ; z ) = 0 , 𝑐 1 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑐 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 𝑐 𝑏 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 1 𝑧 0 {\displaystyle{\displaystyle c(1-z)F\left(a,b;c;z\right)-cF\left(a-1,b;c;z% \right)+(c-b)zF\left(a,b;c+1;z\right)=0,}}
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