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MathGroup Archive 2007

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A Series test

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72765] A Series test
  • From: carlos at colorado.edu
  • Date: Thu, 18 Jan 2007 06:02:29 -0500 (EST)

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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