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.