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MathGroup Archive 1994

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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.





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