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MathGroup Archive 2006

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Re: ArcTan[-Infinity, y] always returning 0?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69855] Re: ArcTan[-Infinity, y] always returning 0?
  • From: "Dave" <daikan1998 at tom.com>
  • Date: Tue, 26 Sep 2006 00:59:10 -0400 (EDT)
  • References: <ef82bq$cuq$1@smc.vnet.net>

It's the seem on my computer with mathematica 5.2. I have tried another
examples. All don't work but one.

\!\(ArcTan[x, y] == \((ArcTan[y\/x] /; y â?? Reals â?§ \(-\(Ï?\/2\)\) <
Arg[x] â?¤ Ï?\/2)\)\)

\!\(ArcTan[x, y] == \((ArcTan[y\/x] + \((2 UnitStep[y] - 1)\) Ï? /;
Element[y, Reals] â?§ Re[x] < 0)\)\)

\!\(ArcTan[x, y] == \((\(Ï?\ \((2\ \@x\^2 - x)\)\)\/\(4\ y\) /; x\^2 ==
y\^2)\)\)

ArcTan[ â??, y] == 0  (*Get True*)

ArcTan[- â??, y] == (2UnitStep[Re[y]] - 1)Ï?



exogen at gmail.com wrote:
> Hi all,
>
> I'm a little confused about the output I'm getting from ArcTan.
>
> According to this page about special values for ArcTan:
> http://functions.wolfram.com/ElementaryFunctions/ArcTan2/03/01/01/0005/
>
> then:
>
> ArcTan[-Infinity, y] == (2 UnitStep[Re[y]] - 1) Pi
>
> However, when I use ArcTan where x is -Infinity, it always returns 0:
>
> In[7]:=
> ArcTan[-Infinity, 1]
>
> Out[7]=
> 0
>
> Shouldn't this return Pi?
>
> The supposed equivalence returns the expected value:
>
> In[11]:=
> (2 UnitStep[Re[1]]-1) Pi
> 
> Out[11]=
> Pi
> 
> 
> Anyone know what's going on?
> 
> Thanks!


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