Re: Difficulties with Complex-Modulus Series

*To*: mathgroup at smc.vnet.net*Subject*: [mg72732] Re: Difficulties with Complex-Modulus Series*From*: dh <dh at metrohm.ch>*Date*: Wed, 17 Jan 2007 06:16:36 -0500 (EST)*References*: <eohtrs$q48$1@smc.vnet.net>

Hi Carlos, $Version 5.1 for Microsoft Windows (October 25, 2004) In this version, Series does not expand Abs[] at all! The reason may be that Series uses D and D can not differentiate Abs. Remember, Abs is not a diferentiable function. Daniel 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. > 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. >