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## #26 2012-12-26 22:00:06

anonimnystefy
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### Re: A nice diophantine equation.

It doesn't!

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #27 2012-12-26 22:06:42

bobbym

Online

### Re: A nice diophantine equation.

Hi;

The gf does not look like the right form to use that formula.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #28 2012-12-26 22:17:22

anonimnystefy
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### Re: A nice diophantine equation.

It is in the right form.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #29 2012-12-26 22:18:46

bobbym

Online

### Re: A nice diophantine equation.

Hmmmm. Then how do you account for the fact that it does not get a good answer?

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #30 2012-12-26 22:21:11

anonimnystefy
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### Re: A nice diophantine equation.

Well, it is an approximation formula... It does no guarantee a close approximation...

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #31 2012-12-26 22:24:05

bobbym

Online

### Re: A nice diophantine equation.

Hi;

That is not correct. The limit of that approximation  divided by the exact answer
should approach 1 as n approaches infinity.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #32 2012-12-26 22:27:40

anonimnystefy
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### Re: A nice diophantine equation.

It should. But, does it?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #33 2012-12-26 22:39:54

bobbym

Online

### Re: A nice diophantine equation.

Hi;

I think this gf

is not in the right form. Look at the formula,

it can not deal with 3 different terms in the denominator. That is why it is not working.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #34 2012-12-27 05:29:32

anonimnystefy
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### Re: A nice diophantine equation.

You can factorise the denominator. You'll have three (1-x) terms. The rest goes into B(x).

And you have copied the required form incorrectly...

Last edited by anonimnystefy (2012-12-27 05:30:39)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #35 2012-12-27 05:34:50

bobbym

Online

### Re: A nice diophantine equation.

Hi;

Are you sure that is not the required form?

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #36 2012-12-27 05:37:41

anonimnystefy
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### Re: A nice diophantine equation.

Yes. But, in either case, A(x) will be the zero polynomial, so they come down to the same thing.

Look at the wiki article to see the correct form.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #37 2012-12-27 05:38:53

bobbym

Online

### Re: A nice diophantine equation.

I can not split that generating function into what you want. Can you show what you did?

The form I have is correct.

http://en.wikipedia.org/wiki/Generating_function

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #38 2012-12-27 05:50:41

anonimnystefy
Real Member

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### Re: A nice diophantine equation.

Those two are not the same...

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #39 2012-12-27 05:52:48

bobbym

Online

### Re: A nice diophantine equation.

Hi;

Yes, you are right! I see that. Very good. But I still think I have you on the gf.

I say that you will be unable to split it as you say.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #40 2012-12-27 06:19:39

anonimnystefy
Real Member

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### Re: A nice diophantine equation.

Hi bobbym

Now we have α=1, β=3, A(x)=0, r=1,

Last edited by anonimnystefy (2012-12-27 06:28:09)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #41 2012-12-27 06:22:02

bobbym

Online

### Re: A nice diophantine equation.

Hi;

I do not think you can do that with B(x).

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #42 2012-12-27 06:24:50

anonimnystefy
Real Member

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### Re: A nice diophantine equation.

Why not? It is analytic...

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #43 2012-12-27 06:26:05

bobbym

Online

### Re: A nice diophantine equation.

When you put that into B(x) you will not get the original gf back.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #44 2012-12-27 06:27:19

anonimnystefy
Real Member

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### Re: A nice diophantine equation.

I do not understand you...

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #45 2012-12-27 06:33:07

bobbym

Online

### Re: A nice diophantine equation.

See what you put into B(x) it does not equal the original generating function. What is in the denominator of your B(x) does not get to the the denominator of the asymptotic form.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #46 2012-12-27 06:34:37

anonimnystefy
Real Member

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### Re: A nice diophantine equation.

Hi bobbym

You didn't substitute the rest of the parameters. α=0, β=3, A(x)=0, r=1.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #47 2012-12-27 06:39:57

bobbym

Online

### Re: A nice diophantine equation.

Hi;

But something is wrong. If you are right you should have got a better answer than you did. I do not understand what is going wrong. I am rechecking everything please hold.

When I make your substitutions I get

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #48 2012-12-27 06:50:39

anonimnystefy
Real Member

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### Re: A nice diophantine equation.

Hi bobbym

Where do you get the x from?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #49 2012-12-27 06:55:10

bobbym

Online

### Re: A nice diophantine equation.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #50 2012-12-27 07:07:57

anonimnystefy
Real Member

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### Re: A nice diophantine equation.

But, with α=0 that will just vanish...

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment