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