       Re: A Series test

• To: mathgroup at smc.vnet.net
• Subject: [mg72771] Re: [mg72765] A Series test
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 19 Jan 2007 01:13:22 -0500 (EST)
• References: <200701181102.GAA01494@smc.vnet.net>

```

On 18 Jan 2007, at 12:02, carlos at colorado.edu wrote:

> 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[Abs][-1]))/a^2,
> (((2*I)/3)*(3 + 6*Derivative[Abs][-1] - 2*Derivative[Abs][-1]))/
>     a^3, (2*(3 + 9*Derivative[Abs][-1] - 6*Derivative[Abs][-1] +
> Derivative[Abs][-1]))/(3*a^4)}, 0, 5, 1]
>
> The correct answer is 1. (The result with Simplify is more
> complicated.)  Thanks.
>

Your code is wrong.
The correct one is:

rho=(x+a*I)/(x-a*I); R=Abs[rho];
s=Series[ComplexExpand[R],{x,0,4}];

Simplify[s,a³0&&x³0]

1

Since you refuse to learn even the most basic things about
Mathematica, it's no wonder it refuses to work the way you want it to.

(However, both the absence of ComplexExpand, about which you have
already been told lots of times and the presence of the totally
pointless Print command, suggest that your only purpose in writing to
this list is to show that you don't care about what others tell you,
no matter how often they do so. But then why do you need to
demonstrate this point so many times?)

Andrzej Kozlowski

```

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