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Re: Difficulties with Complex-Modulus Series


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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Paul Abbott                                      Phone:  61 8 6488 2734
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AUSTRALIA                               http://physics.uwa.edu.au/~paul


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