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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

*Last edited by George,Y (2013-11-07 13:22:56)*

**X'(y-Xβ)=0**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

Hi;

I think you will have to settle for a numerical result. I am not finding a simple form in terms of known constants.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

Yes, that constant is called the nested radical constant, usually denoted C[sub]NR[/sub]. No closed-form expression for that constant currently exists.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

Hi;

Looking at the literature there does not even seem to be a good upper and lower bound.

Also interesting is the Prime Nested Radical

and the Fibonacci Nested Radical

**In mathematics, you don't understand things. You just get used to them.**

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

Alright guys, I think I should give up.

**X'(y-Xβ)=0**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

Hi;

Give up when you have the answer? Why?

**In mathematics, you don't understand things. You just get used to them.**

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**Yusuke00****Member**- Registered: 2013-11-19
- Posts: 43

Guess because he can't understand how u got that results? xD

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

Google and M.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

How do you know which digits are correct?

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

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

I am not following you? The calculation was done by M.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

And you entered what exactly?

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

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

Just what you see in post #2 but to many more iterations.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

Okay, but then, how do you know to how many digits the result is accurate?

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

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

By using the double rule.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

Remind me what that is again.

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

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

You run the calculation to n iterations and then you run it to 2n. You compare digits. I have only ever seen it fail one time.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

When was that?

The next will answer.

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

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

I can not remember, it was a pathological case where someone was making a stupid math point and totally ignoring the thing called practicality.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

You mean, they were specifically looking for a case when it doesn't work?

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

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

Surely you have seen that idiotic example the Borweins came up with?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

No. What was it?

By the way, I am getting

for the first 41 decimal digits.

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

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

So did I.

You did not read about the billion decimal places of pi?

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

Okay, just checking.

I remember reading about BBP type formulas. Has that anything to do with what you are saying?

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

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,691

Yes, he shows a sum that agrees with pi to over 1 billion places and then veers away.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,797

Hm?

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

The knowledge of some things as a function of age is a delta function.

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