*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