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#101 2013-04-17 05:08:45

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Julianthemath's number 3

Can you please compute asymptotic_a[n]-a[n] for a few n and post it here?


“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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#102 2013-04-17 05:14:44

bobbym
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From: Bumpkinland
Registered: 2009-04-12
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Re: Julianthemath's number 3

Can you please compute asymptotic_a[n]-a[n] for a few n and post it here?

I do not understand that. What is a[n]-a[n]?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#103 2013-04-17 05:17:23

anonimnystefy
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Registered: 2011-05-23
Posts: 15,507

Re: Julianthemath's number 3

The first one is asymptotic_a[n], not just a[n].


“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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#104 2013-04-17 05:20:43

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Julianthemath's number 3

Isn't that what the those fractions are in post #98 and 100?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#105 2013-04-17 05:22:39

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Julianthemath's number 3

It is not. Or at least it is not supposed to be. That should be a[n]/asymptotic_a[n].


“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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#106 2013-04-17 05:24:31

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Julianthemath's number 3

Yes, you know what I mean. Okay, I will give the differences.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#107 2013-04-17 05:27:48

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Julianthemath's number 3

Hm, and what do you get for Floor[asymptotic_a[n]] for different n?


“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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#108 2013-04-17 05:32:25

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Julianthemath's number 3


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#109 2013-04-17 05:39:53

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Julianthemath's number 3

Aren't those the sequuence numbers?


“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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#110 2013-04-17 05:41:48

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Julianthemath's number 3

Yes, they are.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#111 2013-04-17 05:44:46

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Julianthemath's number 3

So, we have found a simpler exact form? big_smile


“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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#112 2013-04-17 05:46:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Julianthemath's number 3

Yes but with one problem.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#113 2013-04-17 05:47:28

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Julianthemath's number 3

Which?


“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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#114 2013-04-17 05:48:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Julianthemath's number 3

The floor function is a stepwise function, it is more difficult to work with.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#115 2013-04-17 05:51:26

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Julianthemath's number 3

Yes, but at least it is a bit simpler.


“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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#116 2013-04-17 05:55:18

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Julianthemath's number 3

Some analytical techniques have problems with anything other than a mathematicians dream like smooth functions. To use them you will have to split the recurrence into 4 of them.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#117 2013-04-17 05:58:38

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,507

Re: Julianthemath's number 3

Which analitycal techniques?

Last edited by anonimnystefy (2013-04-17 05:59:02)


“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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#118 2013-04-17 06:04:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 85,265

Re: Julianthemath's number 3

Almost any of them also some M techniques too.

For instance take a try to find the series coefficient with M, with and without the floor function.
One will fail the other will not.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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