Question Number 120554 by snipers237 last updated on 01/Nov/20 | ||
$${Prove}\:{that}\:{for}\:{all}\:\:{a}>\mathrm{0} \\ $$ $$\int_{\left[−{a};{a}\right]} {arg}\left(\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\:−{ix}\right)\right){dx}\:=\mathrm{0} \\ $$ $${Deduce}\:{that}\: \\ $$ $${f}:\:{x}\rightarrow{arg}\left(\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\:−{ix}\right)\right)\:\:{is}\:{an}\:{old}\:{function}\:{on}\:\mathbb{R} \\ $$ | ||