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