Re: Bug with Series[] - help wanted

*To*: mathgroup at smc.vnet.net*Subject*: [mg65411] Re: [mg65394] Bug with Series[] - help wanted*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Fri, 31 Mar 2006 06:09:04 -0500 (EST)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

To enter the input 1+1/r+O((1/r)^2), use Series[1+1/r,{r,Infinity,1}] Another example, Series[1/(r+1),{r,Infinity,3}]//Simplify %//Normal Series[%,{r,Infinity,3}] Bob Hanlon > > From: "GidiL" <gidienator at gmail.com> To: mathgroup at smc.vnet.net > Subject: [mg65411] [mg65394] Bug with Series[] - help wanted > > 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 > 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. > > Can anyone offer some assistance? > > Thanks, > Gideon > >