#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) => UND NO!
Should be INFINITY

Discussion

  • Barton Willis

    Barton Willis - 2003-04-12

    Logged In: YES
    user_id=570592

    Let F : R -> 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

    Logged In: YES
    user_id=588346

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

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

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

    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

    • status: pending --> open
     
  • Stavros Macrakis

    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

    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

    Dieter Kaiser - 2009-12-21

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

     

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