Formula:2651

Digital Library of Mathematical Functions ID 5.8.E1

${\displaystyle{\displaystyle\Gamma\left(z\right)=\lim_{k\to\infty}\frac{k!k^{z}}{z(z+1)\cdots(z+k)},}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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