Convolute two Lorentzain (Cauchy) functions?

Questions
1

I tried

Convolve[PDF[CauchyDistribution[0, mu1], x], PDF[CauchyDistribution[0, mu2], x], x, y]

It does not work.

Any one can give me any thought?

Thanks!

2

It does work for me on:

$Version
(*"11.2.0 for Mac OS X x86 (64-bit) (September 11, 2017)"*)

Taking a bit time to compute though:

conv = Convolve[PDF[CauchyDistribution[0, mu1], x], PDF[CauchyDistribution[0, mu2], x], x, y];

conv // PowerExpand // FullSimplify
\frac{\text{mu1}+\text{mu2}}{\pi \left((\text{mu1}+\text{mu2})^2+y^2\right)}
3

Dear Vitaliy,

Thanks very much for your reply and pointing the usage of PowerExpand as well as FullSimplify to me!

This also works for v10.1

Cheers!

Tony