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#526 2013-12-04 19:15:32

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Series

I don't mind having the discussion.


"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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#527 2013-12-04 22:09:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,681

Re: Series

Thanks gAr.

Can you post the accelerator Borwein found?

I am sure I showed it to you already. I know we discussed it. It is also useless for this sequence. I used Romberg and it worked well.

Want the code for Borwien's?


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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#528 2013-12-04 23:08:24

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

Re: Series

Yes. Is it the one with all the square roots and stuff?


“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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#529 2013-12-04 23:14:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,681

Re: Series

accelerate[n_]:=Module[{d,b,c,s},
d=(3+Sqrt[8])^n;
d=(d+1/d)/2;
b=-1;
c=-d;
s=0;
Table[c=b-c;s=s+c*a[k];b=(k+n)(k-n) b/((k+1/2)(k+1)),{k,0,n-1}];
s/d]

Remember how to use 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.

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#530 2013-12-05 01:20:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

Re: Series

That's the one I was thinking of.

I set a[n] to be the array of the series terms. Then I do N[acc[number_of_terms],number_of_digits.


“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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#531 2013-12-05 01:24:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,681

Re: Series

I am pretty sure it is just for alternating sequences.


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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#532 2013-12-05 01:27:34

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

Re: Series

Yes, I know. It also has to start at 0.


“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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#533 2013-12-05 01:31:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,681

Re: Series

You can adjust the index to handle that. Anyways it is not useful on this 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.

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#534 2013-12-11 10:55:31

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

Re: Series

Hi bobbym

You didn't tell me how we actually get the numerical answer here.

Last edited by anonimnystefy (2013-12-11 10:57:23)


“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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#535 2013-12-11 11:17:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,681

Re: Series

Hi;

See post #527.


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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#536 2013-12-11 11:22:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

Re: Series

Hm, isn't romberg for integrals?


“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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#537 2013-12-11 11:25:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,681

Re: Series

It is for sequences that are the result of numerical integrations on an integral. Actually it is a bunch of sequence accelerators.


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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