Using Residue Theorem To Prove Value Of Summation

[joypav]

View attachment 7345

 

[MarkFL]

Hello!

I just want to point out that uploading images rather than using $\LaTeX$ has some disadvantages. Each user is allowed to upload a certain total number of bytes of attachments (we cannot offer every user unlimited storage space), and so at some point you will run into the ceiling and not be able to upload any more images. Better to be aware of this now rather than to find this out at the point where you cannot upload an image. Also, when people respond to your posts, they cannot use the quote feature to edit your expressions/content...they must instead type everything out themselves.:)

 

[Euge]

Hi joypav,

Note that $\cot \pi z$ has singularities at the integers. What is the residue of $\dfrac{\pi \cot \pi z}{z^2}$ at $z = n$ for some integer $n$?

 

[joypav]

Hello!

I just want to point out that uploading images rather than using $\LaTeX$ has some disadvantages. Each user is allowed to upload a certain total number of bytes of attachments (we cannot offer every user unlimited storage space), and so at some point you will run into the ceiling and not be able to upload any more images. Better to be aware of this now rather than to find this out at the point where you cannot upload an image. Also, when people respond to your posts, they cannot use the quote feature to edit your expressions/content...they must instead type everything out themselves.:)

Yes, I know... I've been wanting to switch over. I use LaTeX some, for school and such, but I just need to look at how to do that here.

I hadn't considered how it would inconvenience you. I am sorry for that! I appreciate all of the help that I have received here.

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Hi joypav,

Note that $\cot \pi z$ has singularities at the integers. What is the residue of $\dfrac{\pi \cot \pi z}{z^2}$ at $z = n$ for some integer $n$?

I got it.. thank you!

 

[MarkFL]

Yes, I know... I've been wanting to switch over. I use LaTeX some, for school and such, but I just need to look at how to do that here.

I hadn't considered how it would inconvenience you. I am sorry for that! I appreciate all of the help that I have received here.

Okay, as long as you're aware of the uploading limit, that was my primary concern...I didn't want you to be "surprised." :) I'm hoping you will find using $\LaTeX$ here is easy, and if you have any questions, please feel free to post here:

http://mathhelpboards.com/math-formulas-mathjax-62/

As for the "inconvenience," that would only pertain to a small number of posts and I didn't mean to make it out as more than it is. Your posting style is excellent otherwise, and normally I would wait until a user has several hundred posts under their belt before "prodding" them to use $\LaTeX$, but I mostly didn't want you to get caught off-guard by the attachment limit. :)