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

*To*: mathgroup at smc.vnet.net*Subject*: [mg70069] Re:ArcTan[-Infinity, y] always returning 0?*From*: dimmechan at yahoo.com*Date*: Mon, 2 Oct 2006 00:33:34 -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 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] 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 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] Pi f[-2] -Pi Anyway I do not consider the subject more. Regards Dimitris