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ArcTan[-Infinity, y] always returning 0?

• To: mathgroup at smc.vnet.net
• Subject: [mg69839] ArcTan[-Infinity, y] always returning 0?
• From: exogen at gmail.com
• Date: Mon, 25 Sep 2006 03:52:56 -0400 (EDT)

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!