Fourier series homework problem

Click For Summary

Homework Help Overview

The discussion revolves around a problem related to finding a closed-form expression for an infinite sum, with references to Fourier series and calculus concepts. Participants express varying levels of familiarity with the necessary mathematical tools, particularly in relation to calculus and series.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the possibility of finding the sum using only calculus II knowledge, with some suggesting that Fourier series may be necessary. Others mention the use of improper integrals as an alternative approach for approximating the sum.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts on the complexity of the problem. Some express uncertainty about the methods available to them, while others provide insights into potential approaches, including approximation techniques. There is no explicit consensus on the best method to find the closed-form solution.

Contextual Notes

Participants note that the original poster is seeking a closed-form solution, which may not be achievable with their current knowledge, particularly due to the presence of the coth function in the expression provided by Wolframalpha.

Bohrok
Messages
867
Reaction score
0
Not really a homework question; I typed this sum into Wolframalpha and it gave a nice, compact expression, but I couldn't figure out where to begin finding it. Is there a way to find it using just calc II-level knowledge of infinite sums?

[PLAIN]http://www4c.wolframalpha.com/Calculate/MSP/MSP839119dd21ei6e3ic70g00005i4356075068c2eb?MSPStoreType=image/gif&s=40&w=264&h=45
 
Last edited by a moderator:
Physics news on Phys.org


Yes. By using a Fourier series.
 


Fourier series are beyond anything I learned in calc II... Is that the only way to do it?
 


Bohrok said:
Fourier series are beyond anything I learned in calc II... Is that the only way to do it?

In many cases, the sum can only be obtained by complicated methods like the Fourier Series. In far more cases, the sum can only be approximated. Personally, I would be happy that this one falls in the first category... but I can see why you would want to be able to do this. I have finished Calc III, and I still don't see a way to do this.
 


The method that you can use which requires only calc I knowledge is using improper integrals for approximating the sum. I saw an example of this on the Stewart (Calc I book which I'm using for my final exam).
 
Telemachus said:
The method that you can use which requires only calc I knowledge is using improper integrals for approximating the sum. I saw an example of this on the Stewart (Calc I book which I'm using for my final exam).

Yes, but that only gives him an approximation. I believe he's looking for a way to retrieve the closed-form solution.
 


Yes, I was looking for a way to find the expression \frac{1}{2}(1 + \pi \coth(\pi)) that Wolframalpha gave for the sum; I kinda figured I couldn't do it yet with that coth in there. I'll just have to wait till Fourier series...
Thanks Char :smile:
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
Replies
6
Views
2K
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 11 ·
Replies
11
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
18
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K