Timeline for Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?
Current License: CC BY-SA 3.0
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| May 19, 2016 at 19:46 | comment | added | Mark Viola | Felix, please don't delete the answer. If we interpret things as generalized functions, then in the spirit of regularization, the limit $\lim_{\rho \to \infty }e^{i\rho}=0$ (Riemann-Lebesgue Lemma) and we are done. -Mark | |
| May 19, 2016 at 19:44 | comment | added | Felix Marin | @Dr.MV Indeed, I'm not happy with my answer since later on I was aware that it was a Fresnel integral. I'll wait 24 hours such that you can read this comment. After that, I'll delete my answer. Thanks a lot. | |
| May 19, 2016 at 18:51 | comment | added | Mark Viola | Hi Felix. There seems to be a flaw in the second step since $\int_0^\infty \rho e^{i\rho^2}\,d\rho$ fails to converge. Since original integral is not absolutely convergent, Fubini-Tonelli does not apply and we cannot assert that the either of the iterated integrals equals the double integral. In this case, apparently, they are not equal. ;-)) ... -Mark | |
| Aug 19, 2013 at 23:20 | history | answered | Felix Marin | CC BY-SA 3.0 |