Question Number 219323 by SdC355 last updated on 23/Apr/25
$${f}\left({s}\right)=\frac{\mathrm{1}}{\mathrm{2}\pi}\:\int\:\:{e}^{−\boldsymbol{{i}}{t}\left({s}−\alpha\right)} \:\mathrm{d}{t}\: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \int_{−\infty} ^{\:+\infty} \:\:{e}^{−\boldsymbol{{i}}{t}\left({s}−\alpha\right)} {e}^{−{sp}} \mathrm{d}{t}\mathrm{d}{s}=? \\ $$