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Re: Difficulties with Complex-Modulus Series



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.

> 



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