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

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)
AUSTRALIA                               http://physics.uwa.edu.au/~paul

```

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