DLMF:15.5.E1 (Q5018)

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DLMF:15.5.E1
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    d d z F ( a , b ; c ; z ) = a b c F ( a + 1 , b + 1 ; c + 1 ; z ) , derivative 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑎 𝑏 𝑐 Gauss-hypergeometric-F 𝑎 1 𝑏 1 𝑐 1 𝑧 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}F\left(a,b;c;z\right% )=\frac{ab}{c}F\left(a+1,b+1;c+1;z\right),}}
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