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Aug 5, 2015 at 10:21 comment added Jean Duchon Yes, but my (maybe naive) hope, through the use of asymptotic analysis, would be that the limit depends on the behavior of the integrand at "decisive points": stationary phase ($\theta=\pi/2$ and $3\pi/2$), maximum amplitude ($\theta=-\pi$), or some optimal trade-off between amplitude and frequency of oscillations.
Aug 4, 2015 at 15:38 comment added user75485 You have also $$ F=e+{1\over{\pi}}Re(\int_0^{\infty} {{e^{it}}\over{\log t +i\pi/2}}dt) $$
Aug 4, 2015 at 12:45 history asked Jean Duchon CC BY-SA 3.0