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Yes, but as long as the imaginary part is there, it is impossible to rule out a doubt (unless you performed other converging methods independently, which you did :-) As far as the Mellin/InverseMellin transform method is concerned, the convincing...
The above can be simplified as follows: PowerExpand[Log[-(1/c)] + Log[c], Assumptions -> Arg[c] > 0] which gives: I Pi As: w[z] = Exp[-z^2] (1 + I Erfi[z]) the expected result follows straightforwardly for Im[z] > 0. ...