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 Jan13 awarded Popular Question Sep24 awarded Autobiographer Sep20 awarded Popular Question Sep20 awarded Yearling Jul27 awarded Notable Question Jul2 awarded Curious Sep11 awarded Popular Question Jul15 awarded Popular Question Apr7 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 Apr7 accepted Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$ Apr7 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 Apr7 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). Apr7 comment Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$ @Raymond Manzoni, can you sketch how you get explicitly that classical integral? Apr7 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 Apr7 comment Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$ It should exist; book claims it is $\sqrt{i \pi / 4b}\, e^{2i\sqrt{ab}}$ Apr7 revised Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$ added 31 characters in body Apr7 asked Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$ Jan14 awarded Yearling Dec13 asked Identity concerning $e^{ia\sin{x}}$ as a series of bessel functions Dec11 accepted Prove summation formula for binomial coefficients