Question Number 87876 by M±th+et£s last updated on 06/Apr/20
$${prove}\:{that} \\ $$ $$\Gamma\left({z}\right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} \:{x}^{{z}−\mathrm{1}} \:{dx},{Re}\left({z}\right)>\mathrm{0} \\ $$
Commented byJoel578 last updated on 07/Apr/20
$$\mathrm{It}\:\mathrm{is}\:\mathrm{a}\:\mathrm{definition},\:\mathrm{thus}\:\mathrm{can}'\mathrm{t}\:\mathrm{be}\:\mathrm{proved} \\ $$