Question Number 29976 by abdo imad last updated on 14/Feb/18
$${prove}\:{that} \\ $$ $${ln}\left(\Gamma\left({x}\right)\right)=\:−{lnx}\:−\gamma{x}\:\:+\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\left(\:\:\frac{{x}}{{n}}\:\:−{ln}\left(\:\mathrm{1}+\frac{{x}}{{n}}\right)\right)\:{with}\:{x}>\mathrm{0} \\ $$