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 Jan 30 awarded Popular Question Sep 9 awarded Nice Question Aug 14 awarded Popular Question Jan 13 awarded Popular Question Sep 24 awarded Autobiographer Sep 20 awarded Popular Question Sep 20 awarded Yearling Jul 27 awarded Notable Question Jul 2 awarded Curious Sep 11 awarded Popular Question Jul 15 awarded Popular Question Apr 7 comment Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$ +1 and very clear answer, but the other one had extra linked material Apr 7 accepted Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$ Apr 7 comment Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$ Incredibly good answer, that's exactly the problem I was trying to do Apr 7 comment Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$ I have the book open in front of me too and there is an $i$, the integral Raymond says is not there. It's the appendix "Some useful definite integrals", integral A.3, emended edition, Dover edition (2010). Apr 7 comment Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$ @Raymond Manzoni, can you sketch how you get explicitly that classical integral? Apr 7 comment Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$ I found this integral in the context of a scattering problem in quantum mechanics. The result is in the appendix to "Quantum Mechanics and Path Integrals", by R.Feynman. I don't know in which sense it converges, hoped some mathematician may know Apr 7 comment Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$ It should exist; book claims it is $\sqrt{i \pi / 4b}\, e^{2i\sqrt{ab}}$ Apr 7 revised Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$ added 31 characters in body Apr 7 asked Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$