Re: A Series test
- To: mathgroup at smc.vnet.net
- Subject: [mg72778] Re: A Series test
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Fri, 19 Jan 2007 01:41:30 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <eonhr6$i8$1@smc.vnet.net>
carlos at colorado.edu wrote:
> Just curious. Could somebody pls run this script on the
> latest Mathematica user version (I think it's 5.2) under
> Windows or Unix and report the results:
>
> rho=(x+a*I)/(x-a*I); R=Abs[rho];
> s=Series[R,{x,0,4}];
> Print[FullSimplify[s,a>=0&&x>=0]//InputForm];
>
> My 5.0 answer (Mac G5 under OS 10.4.8) is
>
> SeriesData[x, 0, {1, (-2*I)/a, (-2*(1 + Derivative[2][Abs][-1]))/a^2,
> (((2*I)/3)*(3 + 6*Derivative[2][Abs][-1] - 2*Derivative[3][Abs][-1]))/
> a^3, (2*(3 + 9*Derivative[2][Abs][-1] - 6*Derivative[3][Abs][-1] +
> Derivative[4][Abs][-1]))/(3*a^4)}, 0, 5, 1]
>
> The correct answer is 1. (The result with Simplify is more
> complicated.) Thanks.
>
In[1]:=
$Version
Out[1]=
"5.2 for Microsoft Windows (June 20, 2005)"
In[2]:=
rho = (x + a*I)/(x - a*I); R = Abs[rho];
s = Series[R, {x, 0, 4}];
Print[InputForm[FullSimplify[s, a >= 0 && x >= 0]]];
From In[2]:=
(a - I*x)/(a + I*x)
(* Why not using ComplexExpand? *)
In[5]:=
ComplexExpand[s]
Out[5]=
1
Regards,
Jean-Marc