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Apr
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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 $\int_0^\infty \exp(ia/x^2+ibx^2)dx$
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asked Integral $\int_0^\infty \exp(ia/x^2+ibx^2)dx$
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asked Identity concerning $e^{ia\sin{x}}$ as a series of bessel functions