I'm trying to compute the following limit:

Limit[ (E^(I t w)) /(2 (-I + 1)), t -> Infinity]

but Mathematica does not compute it. The above limit does not exist, thus I expect that Mathematica gives to me an answer (output) different from the question (input). How can I get the right answer?

Thank you so much for your time.

  • $\begingroup$ Limit[ComplexExpand[(E^(I t w))/(2 (-I+1))], t->Infinity] says this is 1/4 Limit[ Cos[t w]-Sin[t w]+I (Cos[t w]+Sin[t w]), t->Infinity]] and clearly neither the real nor the complex part of that has a limit $\endgroup$ – Bill Jul 29 '18 at 6:14
  • $\begingroup$ What is the result you are expecting? $\endgroup$ – Daniel Lichtblau Jul 29 '18 at 14:30
  • $\begingroup$ Hello @DanielLichtblau, I expect the result "impossible" or something like that (e.g. the limit does not exist). $\endgroup$ – Gennaro Arguzzi Jul 29 '18 at 15:57
  • $\begingroup$ Sometimes Limit returns Indeterminate but offhand I do not know what cases give that result. $\endgroup$ – Daniel Lichtblau Jul 29 '18 at 16:08

The result depends on $w$:

Limit[(E^(I t w))/(2 (-I + 1)), t -> Infinity, Assumptions -> w > 0]


Limit[(E^(I t w))/(2 (-I + 1)), t -> Infinity, Assumptions -> Im[w] > 0]


Limit[(E^(I t w))/(2 (-I + 1)), t -> Infinity,Assumptions -> Im[w] < 0]


| improve this answer | |
  • $\begingroup$ Hello @user64494, I copied your first statement and I got: 1/4 (I E^(2 I Interval[{0, [Pi]}]) + E^(2 I Interval[{0, [Pi]}])). What does E^Interval mean? $\endgroup$ – Gennaro Arguzzi Jul 29 '18 at 6:50
  • $\begingroup$ @Gennaro Arguzzi: This means the set of the limits of the subsequences of (E^(I t w))/(2 (-I + 1)) over all the subsequences t->Infinity. My result is obtained in version 11.3. $\endgroup$ – user64494 Jul 29 '18 at 8:28
  • $\begingroup$ I'm using version 11.2...maybe the result description in 11.3 is better. $\endgroup$ – Gennaro Arguzzi Jul 29 '18 at 16:21

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