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Re: Series[log[x], {x, 0, 3}]

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Am 21.05.2011 12:44, schrieb Hongyi Zhao:
> Hi all,
> 
> I do the following computation within Mathematica:
> 
> Series[log[x], {x, 0, 3}]
> 
> Then I get:
> 
> log[0]+(log^\[Prime])[0] x+1/2 (log^\[Prime]\[Prime])[0] x^2+1/6 (log^(3))
> [0] x^3+O[x]^4
> 
> Any hints on this result?  The log[0] is illegal in my mind.
> 
> Regards.
> --
> .: Hongyi Zhao [ hongyi.zhao AT gmail.com ] Free as in Freedom :.
> 

Hi,

try to use Mathematica Syntax for Log; the outcome is not what you might
expect:

In[1]:= Series[Log[x],{x,0,3}]
Out[1]= Log[x]+O[x]^4

but shifting x by one gives a nice taylor series:

In[2]:= Series[Log[1+x],{x,0,3}]
Out[2]= x-x^2/2+x^3/3+O[x]^4

Peter

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Series[log[x], {x, 0, 3}] Hongyi Zhao <hszhao.cn@gmail.com> - 2011-05-21 10:44 +0000
  Re: Series[log[x], {x, 0, 3}] Erik Max Francis <max@alcyone.com> - 2011-05-22 10:56 +0000
  Re: Series[log[x], {x, 0, 3}] Oliver Jennrich <oliver.jennrich@gmx.net> - 2011-05-22 10:56 +0000
  Re: Series[log[x], {x, 0, 3}] Peter Pein <petsie@dordos.net> - 2011-05-22 10:58 +0000

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