A normalized Series test
- To: mathgroup at smc.vnet.net
- Subject: [mg72756] A normalized Series test
- From: carlos at colorado.edu
- Date: Thu, 18 Jan 2007 05:26:19 -0500 (EST)
Adding to the previous post, my 5.0 result with Normal[] is
rho=(x+a*I)/(x-a*I); R=Abs[rho];
s=Normal[Series[R,{x,0,4}]];
Print[FullSimplify[s,a>=0&&x>=0]//InputForm];
(3*a^4 - (6*I)*a^3*x - 6*a^2*x^2*(1 + Derivative[2][Abs][-1]) + (
2*I)*a*x^3*(3 + 6*Derivative[2][
Abs][-1] - 2*Derivative[3][Abs][-1]) + 2*x^4*(
3 + 9*Derivative[2][Abs][-1] - 6*Derivative[
3][Abs][-1] + Derivative[4][Abs][-1]))/(3*a^4)
Verification that indeed R=1:
Print[FullSimplify[R,a>=0&&x>=0]//InputForm]; (* Simplify fails *)
1
Print[ComplexExpand[R]//InputForm];
1
Interestingly, I ran this script on 2.2 (which still runs under
Classic). The answer is also messy but the Abs argument is +1.