Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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**zetafunc.****Guest**

Maybe everyone is just bored of talking to me. And adriana is too lazy to go through the maths e-mails so she is putting off replying to them, probably.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Is she generally lazy?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

I'm not sure. She washed up all our dishes after we ate at her house, but another time I saw her just drop some food under the sofa (it was a bit of sweetcorn from her pizza) and she didn't bother to pick it up. That was pretty gross. A sign of laziness, maybe?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Girls are a lot sloppier in their habits then they let on.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

She was sloppy, in that case. But I can't think of other encounters where she was.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Sometimes they have closets full of junk. I mean from the floor to the ceiling just stuffed in there. Some of them just throw there clothes around.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

I don't know about that, but she does sometimes go to school in track bottoms or sometimes even pyjamas.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Pajamas? How can you tell?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

She told me. Although most of the time she sleeps in the track-bottoms then goes to school wearing the same ones. She said she doesn't care...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Seems like she is on the carefree side.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

I guess so...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Yes, the modern gal is getting stranger and stranger.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

She was nice to talk to though, even though she is strange. Made many of my otherwise boring days interesting.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

She might come back, who knows. In the meantime forget her.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Easier said than done, I even think about F sometimes.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

I heard she was abducted by aliens and whisked away to Reticulum 4. You might as well forget about her.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

I just need to move on to another girl who interests me, although there aren't any at the moment.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Then turn off the thinking about them. Find something else to occupy your thoughts until one shows up.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Maths reminds me of F sometimes. I can do that though.

I am trying to get to grips with contour integrals but I'm not too sure how they work, my knowledge is pretty limited. Do you know a lot about it?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Not really, I always have had trouble with them too. We could try them together maybe solve a few.

First I have to wash this stack of dishes so I will be back then.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Is the residue of some function f(z) always the co-efficient of 1/(z - a) in its Laurent series? A lot of the time I just end up finding the residue to be zero...

Okay, see you later.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Hi;

They say that it is the coefficient of the

coefficient of the Laurent series, so I would say yes.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

And is it also true that if the residue is 0 then the contour evaluates to 0?

I thought that we had to evaluate 2*pi*i*(sum of the residues)... if the sum of the residues is 0, then...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,786

Hi;

I do not know if that is true.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Okay...

I guess I could try doing something simple like

We know this evaluates to π, so we could maybe try using a contour to try and get the answer too.

Considering instead

where C is a simple closed curve -- a semi-circle in the upper half of the complex plane, from negative infinity to positive infinity, so it encloses the entire real integral, including one of the poles (z = i).

However, I asked Wolfram for the series expansion of 1/(1 + z^2), and it's giving me a series expansion at z = i, and another at z = -i. Since my contour encloses the pole at z = i, I'm interested in the residue of that series.

But I don't know how they found that Laurent series... can you tell me how they found that series expansion that includes the negative power of (z - i)?