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MathGroup Archive 2006

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Re: Bug with Series- help wanted

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65421] Re: Bug with Series- help wanted
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Fri, 31 Mar 2006 06:09:16 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 3/30/06 at 5:29 AM, gidienator at gmail.com (GidiL) wrote:

>Mathematica has a built-in function called Series: Series[x,x_0,n],
>which allows to expand functions into power series where x is the
>variable, x_0 is the point about which we expand, and n is the
>desired order of expansion.

>It also allows x_0 to be infinity, which is very useful when one
>needs multiple expansion (as in gravitational waves and
>electromagnetic radiation).

>Although is allows to expand series in terms of 1/x and writes
>O(1/x) (and its powers) in the output, it does not allow this to be
>entered in the input. To convince yourselves, try it out. Enter in
>the input, e.g., 1+ 1/r+ (O(1/r))^2, and it will tell you that 1/r
>is not a variable.

>If, on the other hand, you entered: In=Series[1/(r+1), {r,
>Infinity,3}]//Simplify you will get
>Out=1/r-(1/r)^2+(1/r)^3+(O(1/r))^4

>which shows that the output is possible, but the input is
>impossible.

Input of a series is very possible. However, as is the case with other things in Mathematica, you cannot simply type an output expression as an input since the displayed output often does not show the entire expression.

To see how to input something equivalent to a given output display the output in either InputForm or FullForm.

To input a series use SeriesData. For example,

In[1]:=
s = SeriesData[x, 0, {1, 1, 1/2, 1/6}, 0, 4, 1]; 

In[2]:=
s == Series[Exp[x], {x, 0, 3}]

Out[2]=
True
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