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.