# Mathematica shuts down when calculating this limit

Bug introduced in 9.0.0 and fixed in 9.0.1

I'm trying to compute this limit:

Limit[E^-(r^2)^(2*n)*r*2*Pi, n -> Infinity]


But, when I run the code above, Mathematica shuts down. I get a warning from Windows stating that the Mathematica 9 Kernel has stopped working. Mathematica itself gives no warning or message. Why is that?

• Which version do you have? Mathematica 9 doesn't crash, although it also can't evaluate this limit. If it's a new crash, you should report this as a bug. Commented Nov 14, 2015 at 18:04
• @OleksandrR. What I get is a warning from windows stating that the MAthematica 9 Kernel has stopped working... Mathematica gives no warning or message Commented Nov 14, 2015 at 18:06
• Are you using 9.0.0? 9.0.1 doesn't seem to have this problem. Commented Nov 14, 2015 at 19:01
• @OleksandrR. yes, 9.0.0 Commented Nov 14, 2015 at 20:16
• I've tagged it as a bug specific to version 9.0.0, because neither 8.0.4 nor 9.0.1 (the previous and next versions, respectively) have the same problem. I suggest updating Mathematica, if you can. Commented Nov 14, 2015 at 22:43

With

 \$Version
(* 10.3.0 for Microsoft Windows (64-bit) (October 9, 2015) *)


Mathemeatica returns a limit that depends on r, as it should.

Plot[Limit[E^-(r^2)^(2*n)*r*2*Pi, n -> Infinity], {r, -2, 2}, AxesLabel -> {r, Lim}]


Although Limit returns unevaluated for arbitrary r, it can be made to produce useful results by making assumptions on r. For instance,
Piecewise[{Assuming[{#}, Limit[E^-(r^2)^(2*n)*r*2*Pi, n -> Infinity]], #} & /@

which reproduces the plot above, apart from the discontinuities at r = -1 and r = 1.
• 9.0.1 can also plot this, although it can't evaluate the limit for arbitrary r. Commented Nov 14, 2015 at 19:02
• @OleksandrR. Sorry for my disjointed response a few hours ago. My plane was about to take off. Indeed, Limit also returns unevaluated for arbitrary r with Mathematica 10.3. But, putting assumptions on it produces useful results, as I just added to my answer. Commented Nov 14, 2015 at 21:50