Difficulties with Complex-Modulus Series

*To*: mathgroup at smc.vnet.net*Subject*: [mg72712] Difficulties with Complex-Modulus Series*From*: carlos at colorado.edu*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.

**Follow-Ups**:**Re: Difficulties with Complex-Modulus Series***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>