Troubleshooting SumConverge in Mathematica

Click For Summary

Discussion Overview

The discussion revolves around troubleshooting the use of the SumConverge function in Mathematica, specifically regarding its ability to determine the convergence of a given series involving an exponential and a sine function. The scope includes technical explanations and user experiences with the software.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant reports that using SumConverge with a specific function results in Mathematica echoing the input, suggesting a potential issue with the command.
  • Another participant suggests that the issue may not be with the n^2 term in the exponential but rather with the sine function, particularly depending on the value of x.
  • A third participant corrects the command to SumConvergence and explains that Mathematica's inability to determine convergence may relate to whether x is a rational multiple of pi.
  • One participant provides a working example using Assuming and FullSimplify, indicating that under the condition t > 0, the function returns True.
  • Another participant expresses frustration at receiving an echo despite following the provided steps, indicating a possible discrepancy in user experience.
  • A later reply suggests verifying the functionality of examples from the help pages for SumConvergence to troubleshoot further.

Areas of Agreement / Disagreement

Participants express differing experiences with the function, with some suggesting that the command is correct while others encounter issues. There is no consensus on the root cause of the problem, and multiple viewpoints on the matter remain unresolved.

Contextual Notes

Limitations include potential dependencies on the specific values of x and t, as well as the version of Mathematica being used, which may affect functionality.

member 428835
Hi PF!

So in mathematica I am trying to see if a function converges so I type: SumConverge[2/(n*Pi) Exp[-n^2*t] Sin[n x], n]

All mathematica does here is echo back what I typed in. Is something I'm doing wrong?

Thanks!
 
Physics news on Phys.org
For the record, there seems to be a problem with the n^2 in the Exp
 
The function you want is SumConvergence, not SumConverge. Usually, when a Mathematica function simply echoes your input that means that it cannot determine the answer.

In this case, the problem isn't the n^2, the problem is the Sin[n x]. If x is some rational multiple of pi then Mathematica can correctly determine that the convergence criteria is Re[t]>0. However, for an arbitrary x or for an x which is not a rational multiple of pi then Mathematica doesn't know, so it returns the input.
 
Last edited:
  • Like
Likes   Reactions: member 428835
Thanks!
 
It just needs a little hint

In[1]:= Assuming[t > 0,
FullSimplify[SumConvergence[2/(n*Pi) Exp[-n^2*t] Sin[n x], n]]]

Out[1]= True
 
I copied what you have and all i received out was an echo... :(
 
Hummm. I reboot the machine. Win7 64, MMA 9 64. Open MMA. Scrape

Assuming[t > 0, FullSimplify[SumConvergence[2/(n*Pi) Exp[-n^2*t] Sin[n x], n]]]

off the screen, paste it into the notebook, <shift><enter> and a few seconds later it replies True.

The result is the same even if you remove the 2/(n*Pi).

If you could reply with your having done exactly those steps, nothing more, and you still get echo then we can try to figure out where to go next.

Unfortunately all the work is done internally and Trace tells us nothing about where it might be going wrong.

You might try all the examples in the help pages for SumConvergence and verify that they work for you.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K