[Maxima-bugs] [ maxima-Bugs-719832 ] limit(exp(x*%i)*x,x,inf) => UND From: SourceForge.net - 2003-04-12 01:39:37 ```Bugs item #719832, was opened at 2003-04-11 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 Category: None Group: None Status: Open Resolution: None Priority: 5 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: 2003-04-11 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: 2003-04-11 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 ```
 [Maxima-bugs] [ maxima-Bugs-719832 ] limit(exp(x*%i)*x,x,inf) => UND From: SourceForge.net - 2003-04-11 17:37:26 ```Bugs item #719832, was opened at 2003-04-11 13:53 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=719832&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 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 ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=719832&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-719832 ] limit(exp(x*%i)*x,x,inf) => UND From: SourceForge.net - 2003-04-12 01:34:17 ```Bugs item #719832, was opened at 2003-04-11 12:53 Message generated for change (Comment added) made by willisb You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=719832&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 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: Barton Willis (willisb) Date: 2003-04-11 20:51 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 ```
 [Maxima-bugs] [ maxima-Bugs-719832 ] limit(exp(x*%i)*x,x,inf) => UND From: SourceForge.net - 2003-04-12 01:39:37 ```Bugs item #719832, was opened at 2003-04-11 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 Category: None Group: None Status: Open Resolution: None Priority: 5 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: 2003-04-11 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: 2003-04-11 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 ```