Complex Variables - Collee level

[andrewanton]

Complex Variables - College level



The first two images describe the background for the problem. The third image has the problem. Any help is greatly appreciated.

 

[Deleted member 4993]

View attachment 2950View attachment 2951View attachment 2952

The first two images describe the background for the problem. The third image has the problem. Any help is greatly appreciated.

I cannot read those images. Please improve contrast and repost. And

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

 

[andrewanton]

The first 3 images are what I have found for the background of the problem. THe problem itself is under problem3 last image.

A latex version of the problem is found in the following website.

http://math.stackexchange.com/questions/417989/dirchlet-problem-and-fourier-series

I cannot read those images. Please improve contrast and repost. And

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

 

[andrewanton]

Latex Version

The latex version of the problem I have posted in the following website.

http://math.stackexchange.com/questions/417989/dirchlet-problem-and-fourier-series

The first 2 images are what I have found for the background of the problem. The third image everything after problem 3 is the question mainly.

Thanks a lot for your help.

 

[Deleted member 4993]

So your problem is:

Show that for N → ∞

\(\displaystyle \displaystyle \int_0^{\infty}\left | \frac{sin[(N+\frac{1}{2})t]}{sin[\frac{t}{2}]}\right |dt\) → ∞



The background work you have shown, does not "really" show any step towards solution to this problem. With that in mind:

Have you tried expanding the numerator?

Please share your work with us.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (e.g. "are these correct?")

 

[andrewanton]

The steps I tried sofar



I think I got the first part of the problem. I have attached it here. I have no clue how to do the integral part and show that as N->infinity the integral of |sin(N+1/2)t/sin(t/2)dt|also goes to infinity. Please help and let me know if the first part is correct.

You are correct the part you mentioned in the previous post is where I am stuck right now. Would you please be lable to give me the stepwise solution. Thanks a lot.