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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,494

Is it possible you are using the wrong poles? That might make the answer change sign.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**zetafunc.****Guest**

I don't think so... type this into Wolfram Alpha:

"residues of the function sqrt(z)/(1+z^3)"

It gives i/3, i/3 and -i/3, the sum of which is i/3.

2iπ(i/3) = -2π/3... but I don't know why.....

**zetafunc.****Guest**

Never mind, I figured it out. It's not me that's wrong, it's Wolfram. The arguments of the poles should all be positive, but for some reason Mathematica doesn't do that.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,494

Those are the correct residues.

I have a worked example using a keyhole contour. It is slightly different than your problem but it might help to clear up what you are doing wrong.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**zetafunc.****Guest**

I think those residues I gave are wrong. If you use positive arguments/angles for the poles (i.e. 5pi/6 instead of -pi/3) you will get the correct residue. The reason for this discrepancy is that Mathematica defines the negative real axis as the branch cut, when it is actually the positive axis.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,494

Okay, glad it worked out.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**zetafunc.****Guest**

The lesson here is that you should never be 100% certain about a CAS's answer... right?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,494

The way I understand it and not too well at that is that M has to make a decision about the branch cuts from a number of choices. They set it up to pick the most useful one. But that may not always be the one you want.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

So it is clearly best to compute the residues for these types of problems by hand, then.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,494

When possible, you should always be checking their results...

For simple poles the residues will not be difficult.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

What I mean is that it is probably best not to tell a CAS to find the residues of f(z). Instead, input the calculation for the residues, so there is no ambiguity. (Or at least, far less.)

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,494

That is how I get mine.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

So what did you need help understanding in my keyhole contour of that problem? I did skip over some steps, I can explain them if it would help.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,494

Hi;

Anything that you would like to add to the original post would be fine for me as well as anyone else.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

I cannot edit posts but I can post it again. What should be added?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,494

HI;

you do not see this at the bottom of your posts?

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

No, I only see the Quote button.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,494

Do you see my avatar?

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

Yes.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,494

I see, it is because you are a guest.

For the keyhole contour you do not have to add anything. It is fine. But if you want to post more about it you can of course.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

I think there might be some keyhole contour problems in the Schaum's book. There is definitely an example in there that uses exactly the same method that I used in that post.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,494

Sorry, I was having back problems and had to get on the floor for a couple of hours.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

What happened?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,494

Nothing yet, I feel pretty bad but I am hungry so I have to get up and sit like a human being.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

You were on the floor for hours? That sounds pretty serious.