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Re: Bug in interpretation of mma Series[] command?


siegman at ee.stanford.edu (A. E. Siegman) wrote:

>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".

Totally disagree!  The fact that the presence of an O[y] term 
AUTOMATICALLY coerces the result into a series is a beautiful and useful 
syntax.  For example, see what happens when you enter

	f[x] + O[x]^5 

>... but the first case should surely
>either generate an error msg, or not be interpreted at
>all.  

Why?

>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.

Yes there is -- whenever you have performed a Series expansion the 
result is a special (SeriesData) object.  Any further manipulutations of 
this object (including muliplying by an arbitrary function) works as 
expected.  E.g.,

	f[x]+O[x]^3

	1/%

I take advantage of this syntax all the time.

Cheers,
	Paul 




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