Prove that $\displaystyle \int_0^{\pi/4} d \phi e^{i \phi} e^{-R^2 \exp{(i 2 \phi)}} = 0$

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- Jan 31st 2013, 11:36 AMstrammerIntegral
Prove that $\displaystyle \int_0^{\pi/4} d \phi e^{i \phi} e^{-R^2 \exp{(i 2 \phi)}} = 0$

- Jan 31st 2013, 03:10 PMchiroRe: Integral
Hey strammer.

Hint: Try using the substitution u = e^(i*theta). - Feb 1st 2013, 02:09 AMJJacquelinRe: Integral
It is not possible to prove it because it is not true :

Another integral - Feb 1st 2013, 05:31 AMstrammerRe: Integral
Pardon me. It is only true as R tends to infinity.

- Feb 1st 2013, 05:56 AMJJacquelinRe: Integral
Obvious !