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Groups > comp.soft-sys.math.mathematica > #2593

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

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Hongyi Zhao wrote:
> 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.

?Series

First, note that `log` has nothing to do with the logarithm function 
`Log`.  As far as Mathematica is concerned, you're referencing an 
unknown function that you just happened to name `log`.  So it should not 
and make any connection between any real-world function.

Second, this is just the standard power series for an arbitrary 
function.  I presume your complaint is that you really meant the 
function to be `Log`, and the logarithm of 0 is undefined, but _you're_ 
the one who specified a Taylor series expansion around x = 0 (a 
Maclaurin series).  So if the function you're thinking of is not defined 
at x = 0, then you shouldn't request the expansion around that point.

-- 
Erik Max Francis && max@alcyone.com && http://www.alcyone.com/max/
  San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
   An undevout astronomer is mad.
    -- Edward Young

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Thread

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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