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#26 2011-08-06 00:19:26

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Getting an asymptotic form for a GF.

Hmmm, I could not numerically integrate a function involving complex numbers.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#27 2011-08-06 00:22:00

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: Getting an asymptotic form for a GF.

Hi gAr;

I think you can in two ways.

1) Sage, Maxima and Wolfram can.

2) Any Newton-Coates formula is just a plug in, so complex numbers are no problem. Remember the answer was in complex form.


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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#28 2011-08-06 01:00:24

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Getting an asymptotic form for a GF.

Hi bobbym,

I still can't do it. Sage demands a real number.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#29 2011-08-06 01:28:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: Getting an asymptotic form for a GF.

Hi gAr;

Okay, it isn't my preferred way of doing it either. Just interesting to see it work.


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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#30 2011-08-06 01:34:41

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Getting an asymptotic form for a GF.

Hi bobbym,

Okay.
Did it work for large coefficients?


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#31 2011-08-06 01:39:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: Getting an asymptotic form for a GF.

Hi gAr;

Yes, but then it becomes a difficult numerical problem.

Was the method I showed in the first post clear enough? Any CAS should be able to do that.


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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#32 2011-08-06 01:47:05

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Getting an asymptotic form for a GF.

Hi bobbym,

Yes, the integral is good!
But I'm not very clear how it got converted to that.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#33 2011-08-06 01:50:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: Getting an asymptotic form for a GF.

Hi gAr;

I am not following you, I meant post #1.


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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#34 2011-08-06 02:01:50

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Getting an asymptotic form for a GF.

Oh, okay.
I was talking about #23.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#35 2011-08-06 02:05:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: Getting an asymptotic form for a GF.

Oh heck, do not worry about that. That is a big mystery to me. How could an integral with complex values zero in on one single coefficient?


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

#36 2011-08-06 02:21:08

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Getting an asymptotic form for a GF.

Yes, a mystery!

That asymptotic form is also mysterious to me.
Can we directly expand about 0 and fit a polynomial?


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#37 2011-08-06 02:25:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: Getting an asymptotic form for a GF.

Hi;

If you expand g(x) around 0 you will have a polynomial, the Taylor polynomial. Trying to truncate that by fitting a smaller polynomial should not work.

In A eq B there is theorem that says the principal part of the Laurents series expansion of g(x) is a good approximation of the coefficients of g(x). That is what I used.


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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#38 2011-08-06 02:35:41

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Getting an asymptotic form for a GF.

Hi,

Okay, I'll check the book.

Thanks.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#39 2011-08-06 02:37:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: Getting an asymptotic form for a GF.

Hi;

Very good! You can help me out with it!


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

#40 2011-08-06 02:39:06

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Getting an asymptotic form for a GF.

Gee, you're kidding again!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#41 2011-08-06 02:40:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: Getting an asymptotic form for a GF.

No kidding! I only get pieces of that book. I am amazingly stupid!


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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#42 2011-08-06 02:46:26

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Getting an asymptotic form for a GF.

Hmmm, we'll see.

I am amazingly stupid!

You're not, otherwise you'd have ruled the nation!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#43 2011-08-06 02:49:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: Getting an asymptotic form for a GF.

Yikes, that is worse! I am not even the best at being an imbecile! I am mediocre!


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

#44 2011-08-06 02:51:40

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Getting an asymptotic form for a GF.

Okay, now I get the estimate!


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#45 2011-08-06 02:54:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: Getting an asymptotic form for a GF.

You got it! Very good. A book showed me a short cut over what I do but I do not remember what it was.


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

#46 2011-08-06 03:05:04

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Getting an asymptotic form for a GF.

Okay.
I guess I have left too much of the book last time I read. I don't remember reading the book at all.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

#47 2011-08-06 03:08:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: Getting an asymptotic form for a GF.

I found it kind of difficult and hard to piece together their algorithms. But it did give me the Hayman method and this 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.

Offline

#48 2011-08-06 03:14:15

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Getting an asymptotic form for a GF.

It's kind of frustrating to read such books.
We'll be dilemma whether to try to read again or skip it, whether the later parts depend on that etc.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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#49 2011-08-06 03:19:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,748

Re: Getting an asymptotic form for a GF.

Books like that should have more examples, a lot more. Math books should be all examples. I was recently looking through an article where the guy was apologizing for explaining his discoveries by examples! The other guys should be apologizing!


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

#50 2011-08-06 03:24:45

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Getting an asymptotic form for a GF.

...the guy was apologizing for explaining his discoveries by examples!

That's funny!

Yes, you are right.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Offline

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