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

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  • Subject: [mg70069] Re:ArcTan[-Infinity, y] always returning 0?
  • From: dimmechan at
  • Date: Mon, 2 Oct 2006 00:33:34 -0400 (EDT)

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

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

However Mathematica (v. 5.2) can somehow 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]

The last option Direction -> -1 with x->-Infinity, may look strange
to someone but it is an undocumented assumption in Limit.
(see e.g


Of course there is a problem since the Limit appeared to be independent
of y which is far
from truth.

Limit[f1[x, -2*y], x -> -Infinity, Direction -> -1]


Anyway I do not consider the subject more.


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