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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Yep, a particularly nasty mess of them too. I got the plates and some pots done.

**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**

How come it is taking you so long?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

My back bothers me the most when doing jobs around that sink. It is too low and I have to bend a lot. I just go slow and get it done in pieces.

**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**

Oh, I see. Would a stool work?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

I do not think so because it would make me taller. The sink was obviously constructed for a smaller person or one with a normal back.

**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**

A lower stool, I mean -- my grandad has one in the bathroom for the sink.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

To sit on or stand on?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

To sit on.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

I wished I had something like that, maybe a bar stool.

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 think PJ has some back problem too.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Anybody can get it regardless of age or shape.

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 feel it too if I bend down for too long, but it is probably not the same thing.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Actually it is quite funny to see all the ugly little kids in the neighborhood staring at me as I lurch and groan while walking down the street. Their mothers say a little prayer as the monster passes them, to protect them. "Your prayers are useless against me you ugly old skank," I scream. "I am not a monster. I am a human being just like you."

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Hmm, never found a Mother literally uttering prayers in such a scenario...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

You have never had me walking through your streets.

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 have seen some pretty scary ones. There is an elderly man who has a terrible back problem walking along my street every morning, he is almost completely keeling over.

Also, have you done the exercise on evaluating definite integrals via contour integration, in the Schaum's Advanced Calculus (3rd edition) book, Ch. 16 pg 434? There are some interesting problems in there that are quite tricky too, and I am stuck on one.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Hi;

Mine is older than that. Let me see if I have the 3rd edition in here.

Okay, I got it. Which number?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Thanks -- question 16.71.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Okay, checking his answer first before we start.

That is correct. What part can we start looking at?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Since x ≥ 0 and f(x) ≥ 0, we should consider a contour such as this:

In other words, the upper right-hand quarter of a circle, enclosing the whole of the first quadrant.

So we have:

.The residue at the pole

is .And that's as far as I've got, because I don't know what to do next...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

I do not think that is right. The correct answer here in my notes is π/3

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

What isn't right?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

My error, you are just computing the pole and the residue so that is correct so far. Excuse the confusion, I am looking at two sets of notes that are not yet cleaned up. This is a work in progress for me.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Any progress?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Yes, I have it done by the residue method.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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