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#51 2011-08-06 03:37:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,292

Re: Getting an asymptotic form for a GF.

Hi;

Anyways, the asymptotic forms come in handy when you can not get an exact answer. The best part about them is that the larger the problem the more accurate they 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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#52 2011-08-06 04:13:22

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

Re: Getting an asymptotic form for a GF.

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."

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#53 2011-08-06 04:18:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,292

Re: Getting an asymptotic form for a GF.

Hi gAr;

See you in a bit, got to do a chore.


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.

Online

#54 2011-08-06 04:18:48

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

Re: Getting an asymptotic form for a GF.

Okay, see you later.


"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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#55 2011-08-10 23:08:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,292

Re: Getting an asymptotic form for a GF.

It is obvious that there is no one way to get these.
A different method might be required each time...

Supposing we start with the GF:

We wish to get the an asymptotic form for the coefficients of z^n

The Wilf partial fraction:

That stumped me for a long time. Since I know Wilf uses maple
he should have at least shown the command that will do this.
He did not and till now I never figured it out.

By using z = {-2,-1,0,1,2,3} we can form the six equations we
need to achieve Wilf's partial fraction.

One of the solutions to this set of simultaneous equations is:

So

No simplifying done to preserve clarity and structure.

Now from expanding manually the coefficient of z^20 is -3968.24698980352. Try g(20)...


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.

Online

#56 2011-08-10 23:21:48

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

Re: Getting an asymptotic form for a GF.

Hi bobbym,

The values are very close! Good one.


"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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#57 2011-08-10 23:33:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,292

Re: Getting an asymptotic form for a GF.

Yes, because the denominator only has one real pole, subtracting it off
which is somehow done with his method. This greatly increases the convergence. The coefficients depend on the singularities of the g(x).


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.

Online

#58 2013-04-07 03:06:35

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,239

Re: Getting an asymptotic form for a GF.

bobbym wrote:

Hi gAr;

You used the Knuth idea to get a smaller recurrence, very good. I am working
on a method that uses residues, it will take a while.

Knuth idea?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#59 2013-04-07 03:14:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,292

Re: Getting an asymptotic form for a GF.

Hi;

It is a Knuth idea that gAr and I were looking at for the gf of the coin problem.


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.

Online

#60 2013-04-07 03:23:01

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,239

Re: Getting an asymptotic form for a GF.

What is that Knuth idea?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#61 2013-04-07 03:25:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,292

Re: Getting an asymptotic form for a GF.

Hi;

I would suggest you get it straight from Knuth.


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.

Online

#62 2013-04-07 03:29:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,239

Re: Getting an asymptotic form for a GF.

Is it in a book?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#63 2013-04-07 03:30:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,292

Re: Getting an asymptotic form for a GF.

Yes, "Concrete Mathematics" Knuth, Graham and Patashnik.


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.

Online

#64 2013-04-07 03:32:06

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,239

Re: Getting an asymptotic form for a GF.

I will have to look at it.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#65 2013-04-07 03:33:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,292

Re: Getting an asymptotic form for a GF.

Do that right now! It is a very good book and you will find it interesting perhaps it will be your favorite.


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.

Online

#66 2013-04-07 03:47:04

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,239

Re: Getting an asymptotic form for a GF.

2nd edition?


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#67 2013-04-07 03:58:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,292

Re: Getting an asymptotic form for a GF.

Yes, p345 on.


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.

Online

#68 2013-04-07 04:13:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,239

Re: Getting an asymptotic form for a GF.

Okay, I just needed to know if that is the one I need to find.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#69 2013-04-07 04:15:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,292

Re: Getting an asymptotic form for a GF.

Yes, 2nd edition get your copy while supplies last.


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.

Online

#70 2013-04-07 04:29:33

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,239

Re: Getting an asymptotic form for a GF.

I have.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#71 2013-04-07 04:36:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,292

Re: Getting an asymptotic form for a GF.

Very good. gAr likes it a little more than I do but we both like 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.

Online

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