I'm trying to integrate the function exp((-2*pi*i*y^2)/m) dy from 0 to inf.
I've tried using the substitution u=y/sqrt(m) but just cannot do it.
Is this integral even possible to evaluate?
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Separate real and imaginary parts. With an adequate substitution you'll obtain the Fresnel integrals.
In M.R. Spiegel - Laplace Transforms - Mc Grow-Hill 1965 You can read... (1)
Setting in (1) and with little computation You [should] obtain... (2)
Let us see if M.R. Spiegel is right
where are the Fresnel integrals. So,
Thanks for this.
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