Difficulties with Complex-Modulus Series

• To: mathgroup at smc.vnet.net
• Subject: [mg72712] Difficulties with Complex-Modulus Series
• Date: Tue, 16 Jan 2007 03:03:33 -0500 (EST)

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.
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.

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