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

*Last edited by George,Y (2012-04-30 19:36:56)*

**X'(y-Xβ)=0**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,722

Hi;

I do not think there are closed forms for either of those. But if you could put some bounds on some of the constants an asymptotic form might be possible.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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

There actually is closed form, but through a different integration.

**X'(y-Xβ)=0**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,722

A different integration?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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

bobbym wrote:

A different integration?

I have found a way to integrate this directly, but it is very tricky.

**X'(y-Xβ)=0**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

I doubt that.

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

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: 103,722

I would say it is unlikely to but the whole question could be answered by posting the solution. Then it can be checked.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

http://m.wolframalpha.com/input/?i=inte … E2&x=0&y=0

*Last edited by anonimnystefy (2013-12-17 01:29:39)*

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

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: 103,722

Hi;

That is not his integral.

But even if it were, that is not in closed form.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

It is not his integral, but his can be manipulated into that one with substitutions and manipulations. The point is that Alpha says there's no closed form...

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

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: 103,722

Hi;

Have you looked at the integral you sent to Alpha in post #8?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Yes, I have.

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: 103,722

Then you know it is not and can never be his integral.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Fixed.

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: 103,722

Brings us back to post #7. The fact that both M's can not do the integral does mean there is a high probability that it is intractable. But they are not infallible, so I think if George would post his answer the whole thing can resolved quickly.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Do you think some progress can be made using DUIT?

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: 103,722

I have not tried but it sure does respond well to numerical integration for any T.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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

Sorry guys, I made a mistake, the question should be:

*Last edited by George,Y (2013-12-29 01:12:55)*

**X'(y-Xβ)=0**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

That does not change much.

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: 103,722

Hi George,Y;

That does not change much.

Yes, I think it is time to show your solution. I am willing to bet 21% of my bankroll, a whopping $1.16 that the solution is wrong.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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

*Last edited by George,Y (2013-12-30 22:11:21)*

**X'(y-Xβ)=0**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,722

Hi;

What is d?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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

After this change of variable, I think now the question is easier.

**X'(y-Xβ)=0**

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

bobbym wrote:

Hi;

What is d?

d is the differential operator

**X'(y-Xβ)=0**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,722

What is the new integral?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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