Troubleshooting SumConverge in Mathematica

[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!

 

[member 428835]

For the record, there seems to be a problem with the n^2 in the Exp

 

[Dale]

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.

 

[member 428835]

Thanks!

 

[Bill Simpson]

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

 

[member 428835]

I copied what you have and all i received out was an echo... :(

 

[Bill Simpson]

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.