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