Mathematica 13.0 does not output the full results of the convolution of a Gaussian with a simple pole.
Integrate[Exp[- x^2 ]/( c - x), {x, -Infinity, Infinity}, PrincipalValue -> True]
gives:
2 Sqrt[Pi] DawsonF[c] if Re[c] > 0 && Im[c] = 0
yet this is incomplete as with Im[z] > 0 one gets a compact expression using the well-known Faddeeva function (pervasive in plasma physics among numerous other fields). The expected result is:
-I Pi w[z]
with w[z] the Faddeeva (or Kramp) function. Mathematica 13.0 boasts having all Ambarowitz and Stegun functions on board (formula 7.1.3). Unfortunately I do not see this well-known function as a Mathematica primitive. It is implemented in MATLAB or Octave, though.
Or did I miss something?
