Re: Bug with Series[] - help wanted

• To: mathgroup at smc.vnet.net
• Subject: [mg65410] Re: [mg65394] Bug with Series[] - help wanted
• From: "Carl K. Woll" <carlw at wolfram.com>
• Date: Fri, 31 Mar 2006 06:09:04 -0500 (EST)
• References: <200603301029.FAA18297@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```GidiL wrote:
> Hello all!
>
> I would really appreciate some help.
>
> 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
>
> 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.
>
> Can anyone offer some assistance?
>
> Thanks,
> Gideon

Gideon,

Use the 2-argument form of O:

In[1]:=
O[r,Infinity]^4

Out[1]=
O[1/r]^4

Carl Woll
Wolfram Research

```

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