See my following testing:
In[140]:= Limit[(1+ I \[Theta]/x)^x,x->Infinity]/.{I \[Theta]->x}
Series[%, {x, 0, 10}]/.{x-> I \[Theta]}
Out[140]= E^x
During evaluation of In[140]:= SeriesData::sdatv: First argument I \[Theta] is not a valid variable.
Out[141]= SeriesData[Complex[0, 1] \[Theta], 0, {1, 1,
Rational[1, 2],
Rational[1, 6],
Rational[1, 24],
Rational[1, 120],
Rational[1, 720],
Rational[1, 5040],
Rational[1, 40320],
Rational[1, 362880],
Rational[1, 3628800]}, 0, 11, 1]
Why will the "SeriesData::sdatv: First argument I [Theta] is not a valid variable." be triggered in this case, and how to fix it?
Regards, Zhao