1)
2)
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I can evaluate all of these integrals, but using a method that's just too difficult to justify. Namely evaluating an integral with real-valued parameters and assuming the solution is valid when one of the parameters is imaginary.
1)
2)
3)
4)
I can evaluate all of these integrals, but using a method that's just too difficult to justify. Namely evaluating an integral with real-valued parameters and assuming the solution is valid when one of the parameters is imaginary.
I am out of my depth here, but have an idea.
The solution is clearly real.
What if we consider the complex integral:
; where I assume a,b are real and z = x + iy
Now
when x = y.
also
tends to zero, when x is sufficiently large
So if we integrate along the path from the origin out to (R + iR) and then around the arc (centred on the origin) from R+iR to we find, after taking R to the limit of infinity, that the solution is zero.