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RE: Unexpected behavior with S

• To: mathgroup@smc.vnet.net
• Subject: [mg11958] RE: [mg11942] Unexpected behavior with S
• From: Ersek_Ted%PAX1A@mr.nawcad.navy.mil
• Date: Fri, 10 Apr 1998 01:03:47 -0400

Adrian Cable  wrote:
|
|In fact, it turns out that for any integer k,
|(Series[x^x,{x,0,k}]-1)/(Log[x]) = Integrate[Series[x^x,{x,0,k}]].
Now, |this result doesn't make sense, because it would imply that
|Integrate[x^x,x] = (x^x - 1)/Log[x], whereas in fact Integrate[x^x,x]
|cannot be expressed in closed form. What have I (or Mathematica, for
|that matter) done wrong here to get this obviously incorrect result? |
|
   I looked into it, and it may be that Mathematica incorrectly does the
integral for certain cases of SeriesData (a series expansion with an
O[x]^n  term).  See below.

I may have missed something, but I would expect zero for Out[2] and
Out[3]  below.


In[1]:=
poly=Series[x^x, {x,0,2}];
int=Integrate[poly, x];


In[2]:=
Normal[ D[int, x] - poly ]

Out[2]=
x/2


In[3]:=
D[ Normal[int], x ] - Normal[poly]

Out[3]=
x/2 + 1/3*x^2*Log[x]


Ted Ersek