Re: polynomial division
- To: mathgroup at smc.vnet.net
- Subject: [mg41943] Re: polynomial division
- From: Marian Otremba <marianUSUN at zeus.polsl.gliwice.pl>
- Date: Wed, 11 Jun 2003 03:49:32 -0400 (EDT)
- References: <bbmu7c$ju$1@smc.vnet.net> <bbq6eu$csv$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
oldodo2000 wrote:
>> How can I find an approximation of the result of g(x)=1/(x^2+x+1)
Bob Hanlon wrote:
>
> n=4;
>
> Series[1/(x^2+x+1), {x,0,n}]//Normal
>
> -x^4 + x^3 - x + 1
>
OK if x<<1
for example
n=6;
p=x^2+x+1;
w1=Series[1/p,{x,0,n}] // Normal
Plot[1/p-w1,{x,0,1/2},PlotRange->All]
if x >>1
w2=(Series[(1/p) /. x->1/u,{u,0,n}]//Normal) /. u->1/x
Plot[1/p-w2,{x,2,5},PlotRange->All]
if x about 1
w3=((Series[(1/p) /. x->1/(u+1),{u,0,n}]//Normal) /. u->1/x-1)//Expand
Plot[1/p-w3,{x,2/3,2},PlotRange->All]
--
marian otremba