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From: SourceForge.net <noreply@so...>  20091221 01:44:26

Bugs item #719832, was opened at 20030411 19:53 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=719832&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core  Limit Group: None >Status: Pending >Resolution: Works For Me Priority: 5 Private: No Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: limit(exp(x*%i)*x,x,inf) => UND Initial Comment: limit(exp(x*%i)*x,x,inf) => UND NO! Should be INFINITY  >Comment By: Dieter Kaiser (crategus) Date: 20091221 02:44 Message: 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  Comment By: Stavros Macrakis (macrakis) Date: 20030412 03:55 Message: 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  Comment By: Barton Willis (willisb) Date: 20030412 03:51 Message: 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  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=719832&group_id=4933 
From: SourceForge.net <noreply@so...>  20091221 11:54:31

Bugs item #719832, was opened at 20030411 13:53 Message generated for change (Comment added) made by macrakis You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=719832&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core  Limit Group: None >Status: Open Resolution: Works For Me Priority: 5 Private: No Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: limit(exp(x*%i)*x,x,inf) => UND Initial Comment: limit(exp(x*%i)*x,x,inf) => UND NO! Should be INFINITY  >Comment By: Stavros Macrakis (macrakis) Date: 20091221 06:54 Message: 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).  Comment By: Dieter Kaiser (crategus) Date: 20091220 20:44 Message: 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  Comment By: Stavros Macrakis (macrakis) Date: 20030411 21:55 Message: 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  Comment By: Barton Willis (willisb) Date: 20030411 21:51 Message: 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  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=719832&group_id=4933 
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