Comparison of normalised Lorentzian (or Cauchy) and Gaussian distributions, with FWHM, Gamma, = 2.354 sigma.
Applies to natural line profiles, collisional broadening and to Fabry-Perot etalons.
.
The mean is 
and the half-width is 
. This distribution
has very extended wings and indeed 
is not defined as the
integral is unbounded!