ROOT prints error: ERROR 26 :
Unknown name : "gauss"
Error in TF1::TF1: function: TF1_ExpValHelper/g1pow(x,1.000000) has 0 parameters instead of 1
mean = 1.79511e-269

Currently TF1::Mean (and TF1::Moment) can only be used if the TF1 is based solely on the string version of TFormula (i.e. not your case; you have a TF1 based on a C++ function). There is currently no work-around (you might be able to populate an histogram with your value and get the mean for it).