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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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]?

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**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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The first one is asymptotic_a[n], not just a[n].

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,685

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Hm, and what do you get for Floor[asymptotic_a[n]] for different n?

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**bobbym****Administrator**- From: Bumpkinland
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**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
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Aren't those the sequuence numbers?

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**bobbym****Administrator**- From: Bumpkinland
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Yes, they are.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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So, we have found a simpler exact form?

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**bobbym****Administrator**- From: Bumpkinland
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Yes but with one problem.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Which?

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**bobbym****Administrator**- From: Bumpkinland
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The floor function is a stepwise function, it is more difficult to work with.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Yes, but at least it is a bit simpler.

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**bobbym****Administrator**- From: Bumpkinland
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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.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Which analitycal techniques?

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

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**bobbym****Administrator**- From: Bumpkinland
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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.

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