## #296 limit(exp(x*%i)*x,x,inf) should give infinity

open
nobody
5
2009-12-21
2003-04-11
No

limit(exp(x*%i)*x,x,inf) =&gt; UND NO!
Should be INFINITY

## Discussion

• Barton Willis - 2003-04-12

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Let F : R -&gt; C and F(x) = x exp(i x) = x cos(x) + i x sin(x).
Both the real and imaginary parts of F are oscillatory with
linearly growing amplitudes; neither the real nor the imaginary
parts have a limit towards infinity. I say the limit is UND.

Barton

• Stavros Macrakis - 2003-04-12

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I believe that the definition of limit(f(x))=infinity is that for all N,
there exists an X such that x&gt;X implies abs(f(x))&gt;N.

That is satisfied in this case. In fact, you can choose X=N.
The separate magnitudes of the real and imaginary parts are
irrelevant.

After all, limit(2+x*%i,x,inf) = infinity

• Robert Dodier - 2006-04-09
• labels: --> Lisp Core - Limit

• Dieter Kaiser - 2009-12-21
• status: open --> pending

• Dieter Kaiser - 2009-12-21

The example of this bug report gives no longer 'und but a noun form (Maxima 5.20post);

(%i11) limit(exp(x*%i)*x,x,inf);
(%o11) 'limit(x*%e^(%i*x),x,inf)

I am not sure what is the right answer. Wolfram alpha gives a result in terms of an interval:

E^((2 I) Interval[{0, Pi}]) Infinity

A noun form is not a wrong result. Perhaps, we can close this bug report at this point. Further improvements of the limit routines might give a more complete answer.
Setting the status to pending and the resolution to "works for me".

Dieter Kaiser

• Stavros Macrakis - 2009-12-21
• status: pending --> open

• Stavros Macrakis - 2009-12-21

A noun form is certainly better than und, but the correct result is Infinity. I would have thought that in the Wolfram world, the correct result would be ComplexInfinity (which corresponds to Maxima's Infinity).

• Dieter Kaiser - 2009-12-21
• summary: limit(exp(x%i)x,x,inf) => UND --> limit(exp(x%i)x,x,inf) should give infinity

• Dieter Kaiser - 2009-12-21

Changing the title to reflect the issue better. Setting the resolution back to "None".
Dieter Kaiser