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!