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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg119115] Re: Series[log[x], {x, 0, 3}]
  • From: Erik Max Francis <max at alcyone.com>
  • Date: Sun, 22 May 2011 06:54:58 -0400 (EDT)
  • References: <ir8534$ba5$1@smc.vnet.net>

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 at 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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