Question Number 27496 by abdo imad last updated on 07/Jan/18
$${let}\:{give}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\propto} \:\:\frac{\mathrm{1}}{\sqrt{{t}}}\:{e}^{−\left(\mathrm{1}+{ix}\right){t}} {dt} \\ $$$${calculate}\:{f}^{'} \left({x}\right)\:{prove}\:{that}\:\exists\lambda\in{R}/\left({x}+{i}\right)^{\mathrm{2}} \:\left({f}\left({x}\right)\right)^{\mathrm{2}} =\:\lambda \\ $$$${then}\:{find}\:\:\int_{\mathrm{0}} ^{\propto} \:\:{e}^{−{t}^{\mathrm{2}} } {dt}\:. \\ $$