Formula:5886

Digital Library of Mathematical Functions ID 16.3.E2

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \deriv[n]{}{z}\left(z^{\gamma}\genhyperF{p}{q}@@{a_{1},\dots,a_{p}}{b_{1},\dots,b_{q}}{z}\right)=\Pochhammersym{\gamma-n+1}{n}z^{\gamma-n}\genhyperF{p+1}{q+1}@@{\gamma+1,a_{1},\dots,a_{p}}{\gamma+1-n,b_{1},\dots,b_{q}}{z},}

Symbols List

• ${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}$: alternatively F q p ( a ; b ; z ) or F q p ( a b ; z ) generalized hypergeometric function
• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle p}}$: nonnegative integer
• ${\displaystyle{\displaystyle q}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}$: real or complex parameters
• ${\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}$: real or complex parameters
 

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