       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

> 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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