Formula:2697

Digital Library of Mathematical Functions ID 5.9.E19

${\displaystyle{\displaystyle{\Gamma^{(n)}}\left(z\right)=\int_{0}^{\infty}(\ln t)^{n}e^{-t}t^{z-1}\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle\Re z>0}}$
${\displaystyle{\displaystyle n\geq 0}}$
${\displaystyle{\displaystyle\Re z>0}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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