Series involving logarithms

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Series involving logarithms*From*: belopols at marie.mit.edu (Alexander Belopolsky)*Date*: Mon, 2 May 1994 19:18:30 -0400

Dear MathGroup, Mathematica 2.2 apparently support the series involving logarithms: Mathematica 2.2 for DEC RISC Copyright 1988-93 Wolfram Research, Inc. -- Terminal graphics initialized -- In[1]:= Series[x^x,{x,0,4}] 2 2 3 3 4 4 Log[x] x Log[x] x Log[x] x 5 Out[1]= 1 + Log[x] x + ---------- + ---------- + ---------- + O[x] 2 6 24 I would expect that Logs be treated as constants when they appear in a series. So far I would expect that Log[1+x Log[x] + O[x]^2] = x Log[x] + O[x]^2, but In[2]:= Log[1 + x Log[x] + O[x]^2] 2 Series::lss: Logarithmic singularity encountered in Log[1 + Log[x] x + O[x] ]. 2 Out[2]= Log[1 + Log[x] x + O[x] ] It is strange because Log is analytic near 1, it is as good as Exp near 0, yet for Exp there is no problem: In[2]:= Exp[x Log[x] + O[x]^2] 2 Out[2]= 1 + Log[x] x + O[x] Does anyone know how the Series::lss message is generated and is there any way to teach mathematica to deal with logarithms properly rather then substitute them by constants in the intermediate calculations? Alexander Belopolsky.