Re: Series[log[x], {x, 0, 3}]
- To: mathgroup at smc.vnet.net
- Subject: [mg119128] Re: Series[log[x], {x, 0, 3}]
- From: Peter Pein <petsie at dordos.net>
- Date: Sun, 22 May 2011 06:57:19 -0400 (EDT)
- References: <ir8534$ba5$1@smc.vnet.net>
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