Re: Difficulties with Complex-Modulus Series
- To: mathgroup at smc.vnet.net
- Subject: [mg72731] Re: Difficulties with Complex-Modulus Series
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Wed, 17 Jan 2007 06:12:35 -0500 (EST)
- Organization: The University of Western Australia
- References: <eohtrs$q48$1@smc.vnet.net>
In article <eohtrs$q48$1 at smc.vnet.net>, carlos at colorado.edu wrote:
> Say I have r = (2*I+x)/(2*I-x), in which x is real and nonnegative.
>
> Series[r,{x,0,4}] and Series[r,{x,Infinity,4}] work as expected.
>
> Introduce now R=Abs[r] and try the same:
>
> Series[R,{x,0,4}] and Series[R,{x,Infinity,4}]
> Results are now "contaminated" with Abs'[-1], Abs''[-1], etc,
> I dont understand the presence of those derivatives.
I don't get this behavior in 5.2.
> Anybody can explain the reason? (I teach students that the
> derivative of a constant is zero, but perhaps that has changed
> with the new year) BTW it would be nice to say
>
> Series[R,{x,0,4}, x>=0] or Series[R,{x,0,4}, R>=0] etc
>
> if that would get rid of the garbage, but Mathematica 5
> does not allow Assumptions in Series. Note BTW that R=1 for
> any x, so the R series are in fact trivial to any order.
Of course -- so, since x is real why not use
R = ComplexExpand[ Abs[r] ]
Cheers,
Paul
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