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Bug in interpretation of mma Series[] command?


Does the following make sense to anyone?

   In[6]:=
   f[y] = Exp[-a y^2] * Series[1/(1 + y^2), {y,0,5}]
   
   Out[6]=
                               2
                 2            a    4       6
   1 + (-1 - a) y  + (1 + a + --) y  + O[y]
                              2

This strikes me as a really counter-intuitive, perverse,
guaranteed-to-cause-trouble "gotcha".  

I have to agree that 

   In[7]:=
   f[y] = Exp[-a y^2] * Normal[Series[1/(1 + y^2), {y,0,5}]]

   Out[7]=
        2    4
   1 - y  + y
   -----------
          2
       a y
      E

does what's expected; but the first case should surely
either generate an error msg, or not be interpreted at
all.  There's no way any sensible interpretation of
the input command (by normal users, that is) should lead
to series expansion of the Exp[] function also.


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