Formula:2667

Digital Library of Mathematical Functions ID 5.9.E4

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

Constraint(s)

${\displaystyle{\displaystyle z\neq 0,-1,-2,\dots}}$

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
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

Resources that cite this formula

No records found.