Re: series expansion of polys with real exponents
- To: mathgroup@smc.vnet.net
- Subject: [mg11674] Re: [mg11656] series expansion of polys with real exponents
- From: Bob Hanlon <BobHanlon@aol.com>
- Date: Sat, 21 Mar 1998 18:35:11 -0500
A partial series is given by
Normal[Series[(2*x^5)/(2 - x - x^9), {x, 0, 16}]]
(769*x^16)/2048 + (513*x^15)/1024 + (257*x^14)/512 +
x^13/256 + x^12/128 + x^11/64 + x^10/32 + x^9/16 + x^8/8 +
x^7/4 + x^6/2 + x^5
PowerExpand[% /. x -> D^0.2]
(769*D^3.2)/2048 + (513*D^3.)/1024 + (257*D^2.8)/512 +
D^2.6/256 + D^2.4/128 + D^2.2/64 + D^2./32 + D^1.8/16 +
D^1.6/8 + D^1.4/4 + D^1.2/2 + D^1.
N[%]
0.37548828125*D^3.2 + 0.5009765625*D^3. +
0.501953125*D^2.8 + 0.00390625*D^2.6 + 0.0078125*D^2.4 +
0.015625*D^2.2 + 0.03125*D^2. + 0.0625*D^1.8 +
0.125*D^1.6 + 0.25*D^1.4 + 0.5*D^1.2 + D^1.
This would appear to require that Abs[D] < 1
Bob Hanlon
In a message dated 3/20/98 12:02:54 AM, rauf@eecs.umich.edu wrote:
>I would like to find the series expansion of an expression like
>
>2 D / (2 -D^0.2 -D^1.8)
>
>in positive (real) powers of D. As the expression has real exponents on
>D, it's not really a polynomial and none of the polynomial functions
>work here. Is there any way to work it out?