Question Number 120554 by snipers237 last updated on 01/Nov/20
![Prove that for all a>0 ∫_([−a;a]) arg(Γ((1/2) −ix))dx =0 Deduce that f: x→arg(Γ((1/2) −ix)) is an old function on R](https://www.tinkutara.com/question/Q120554.png)
$${Prove}\:{that}\:{for}\:{all}\:\:{a}>\mathrm{0} \\ $$$$\int_{\left[−{a};{a}\right]} {arg}\left(\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\:−{ix}\right)\right){dx}\:=\mathrm{0} \\ $$$${Deduce}\:{that}\: \\ $$$${f}:\:{x}\rightarrow{arg}\left(\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\:−{ix}\right)\right)\:\:{is}\:{an}\:{old}\:{function}\:{on}\:\mathbb{R} \\ $$