Formula:2669

Digital Library of Mathematical Functions ID 5.9.E5

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

Constraint(s)

${\displaystyle{\displaystyle-n-1<\Re z<-n}}$

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
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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