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

• To: mathgroup at smc.vnet.net
• Subject: [mg70068] Re:ArcTan[-Infinity, y] always returning 0?
• From: dimmechan at yahoo.com
• Date: Mon, 2 Oct 2006 00:33:33 -0400 (EDT)

This is a reply to a one week's post from exo... at gmail.com

As I read on others' replies there is a bug.

However Mathematica (v. 5.2) can return the right answer
working as follows (which sounds normal to me since you
deal with the Infinity)

f1[x_, y_] := ArcTan[x, y]
f2[y_] := (2*UnitStep[Re[y]] - 1)*Pi

Limit[f1[x, y], x -> -Infinity, Direction -> -1]
Pi

The last option Direction -> -1 with x->-Infinity, may look strange
to someone but it is an undocumented assumption in Limit.
(see e.g
http://groups.google.gr/group/comp.soft-sys.math.mathematica/browse_thread/thread/bcab1674a3cfcc44/1834204792733e57?lnk=gst&q=undocumented&rnum=8#1834204792733e57)

f2[1]
Pi

Regards
Dimitris