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#9426 2013-03-22 03:53:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Linear Interpolation FP1 Formula

That is correct.

For  the second limit?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9427 2013-03-22 03:58:33

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

#9428 2013-03-22 04:00:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Linear Interpolation FP1 Formula

That is correct.

Now you have to add them, what did you get?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9429 2013-03-22 04:04:41

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Adding and then multiplying by 2*pi*i, I get

#9430 2013-03-22 04:12:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Linear Interpolation FP1 Formula

You only multiply by π i, see post #9420.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9431 2013-03-22 04:13:47

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Why? I thought it was 2*pi*i*(sum of the residues), not pi*i...

#9432 2013-03-22 04:15:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Linear Interpolation FP1 Formula

Yes, but that is from -∞ to ∞. This integral is symmetrical and goes from 0 to ∞.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#9433 2013-03-22 04:24:59

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Oh, okay...

Also, I get the same answer as you but only if I take the real part of my answer and ignore the imaginary part. Am I supposed to do that or is that just an error in my arithmetic?

#9434 2013-03-22 04:32:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Linear Interpolation FP1 Formula

Something is wrong with the arithmetic. What are you using to compute the sum of the two limits?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9435 2013-03-22 04:34:15

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Hmm, WolframAlpha is getting the right answer, so there is a problem with me, I'll check my arithmetic again.

#9436 2013-03-22 04:39:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Linear Interpolation FP1 Formula

Okay, I am going to have to get some sleep. See you later. You should be able to do some others using this same method.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9437 2013-03-22 06:40:50

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Okay, see you later.

I got it, I was being silly, it is not the arithmetic that is an issue -- I just wasn't using De Moivre's to get the complex number form of those powers of i. This is a great technique, I will try it out on some other interesting integrals.

#9438 2013-03-22 11:32:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Linear Interpolation FP1 Formula

Hi;

For the simple poles it is really easy.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#9439 2013-03-22 11:45:56

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I tried it for something like

and I cannot get it to work...

#9440 2013-03-22 11:51:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Linear Interpolation FP1 Formula

What did you get for that one?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#9441 2013-03-22 12:03:38

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I am getting the residue to be zero but I am guessing I need to do something else... there is only one pole and it is a removable singularity (no C[sub]-1[/sub] co-efficient in the Laurent series). The answer should be \pi and DUIS can be used to show this, but I wanted to approach it with contour integration.

#9442 2013-03-22 12:08:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Linear Interpolation FP1 Formula

Yes, no Laurent series. I am getting zero also. It is obviously wrong so this method might not apply here


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#9443 2013-03-22 12:19:59

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I remember reading some PDF where a guy managed to do it but I can't remember what he did...

I think there is something missing in our methodology -- aren't there a number of steps that have to be done first, e.g. showing that the function is holomorphic?

#9444 2013-03-22 12:27:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Linear Interpolation FP1 Formula

Yes, I believe so. Are you sure you could do it using Residues? This one does not have a Laurent series. Doesn't that mean no poles?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#9445 2013-03-22 12:31:54

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

But that function is clearly not defined at x = 0... surely it has a pole there? What else would be there? I thought that if it doesn't appear in the series expansion about that point, then it just means that it is a removable singularity.

#9446 2013-03-22 12:34:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Linear Interpolation FP1 Formula

A pole is the coefficient of the a(-1) term. There is no such term here.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#9447 2013-03-22 12:38:40

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I thought that was the residue?

#9448 2013-03-22 12:45:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Linear Interpolation FP1 Formula

Oh excuse me, I meant residue. If the residue is 0 then the integral is 0 according to that formula.

0 is a removable singularity but it is not a pole.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#9449 2013-03-22 12:48:45

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

But this integral is π, not zero... what do we do?

#9450 2013-03-22 12:50:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Linear Interpolation FP1 Formula

Have to find another way to evaluate it. What I am saying is that for some reason this method does not apply here. Possibly because it has no Laurent series.

http://mathworld.wolfram.com/Pole.html

Second paragraph helps.

Last edited by bobbym (2013-03-22 12:58:33)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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