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RE: A Series test

• To: mathgroup at smc.vnet.net
• Subject: [mg72777] RE: [mg72765] A Series test
• From: "Virgilio, Vincent - SSD" <Vincent.Virgilio at itt.com>
• Date: Fri, 19 Jan 2007 01:37:29 -0500 (EST)

Mathematica 5.2.0.0 on Win XP gives:

(a - I*x)/(a + I*x) 

-----Original Message-----
From: carlos at colorado.edu [mailto:carlos at colorado.edu] 
Sent: Thursday, January 18, 2007 6:02 AM
To: mathgroup at smc.vnet.net
Subject: [mg72777] [mg72765] A Series test

Just curious. Could somebody pls run this script on the latest
Mathematica user version (I think it's 5.2) under Windows or Unix  and
report the results:

rho=(x+a*I)/(x-a*I); R=Abs[rho];
s=Series[R,{x,0,4}];
Print[FullSimplify[s,a>=0&&x>=0]//InputForm];

My 5.0 answer (Mac G5 under OS 10.4.8) is

SeriesData[x, 0, {1, (-2*I)/a, (-2*(1 + Derivative[2][Abs][-1]))/a^2,
(((2*I)/3)*(3 + 6*Derivative[2][Abs][-1] - 2*Derivative[3][Abs][-1]))/
    a^3, (2*(3 + 9*Derivative[2][Abs][-1] - 6*Derivative[3][Abs][-1] +
Derivative[4][Abs][-1]))/(3*a^4)}, 0, 5, 1]

The correct answer is 1. (The result with Simplify is more
complicated.)  Thanks.

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