DLMF:16.3.E1 (Q5188)

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DLMF:16.3.E1
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    d n d z n F q p ( a 1 , , a p b 1 , , b q ; z ) = ( 𝐚 ) n ( 𝐛 ) n F q p ( a 1 + n , , a p + n b 1 + n , , b q + n ; z ) , derivative 𝑧 𝑛 Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 subscript 𝑎 𝑝 subscript 𝑏 1 subscript 𝑏 𝑞 𝑧 Pochhammer 𝐚 𝑛 Pochhammer 𝐛 𝑛 Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 𝑛 subscript 𝑎 𝑝 𝑛 subscript 𝑏 1 𝑛 subscript 𝑏 𝑞 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}{{}_{p}F% _{q}}\left({a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}};z\right)=\frac{{\left(% \mathbf{a}\right)_{n}}}{{\left(\mathbf{b}\right)_{n}}}{{}_{p}F_{q}}\left({a_{1% }+n,\dots,a_{p}+n\atop b_{1}+n,\dots,b_{q}+n};z\right),}}
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    DLMF:16.3.E1
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