DLMF:15.5.E3 (Q5020)

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DLMF:15.5.E3
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    test
    ( z ⁢ d d z ⁡ z ) n ⁢ ( z a - 1 ⁢ F ⁡ ( a , b ; c ; z ) ) = ( a ) n ⁢ z a + n - 1 ⁢ F ⁡ ( a + n , b ; c ; z ) . superscript 𝑧 derivative 𝑧 𝑧 𝑛 superscript 𝑧 𝑎 1 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 Pochhammer 𝑎 𝑛 superscript 𝑧 𝑎 𝑛 1 Gauss-hypergeometric-F 𝑎 𝑛 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(z^{a-1}F\left(a,b;c;z\right)\right)={\left(a\right)_{n}}z^{a+n-1}F\left(% a+n,b;c;z\right).}}
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    DLMF id
    DLMF:15.5.E3
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