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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,656

Have you ever seen anonimnystefy's problem that he posed a while back?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Which problem is that?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,656

http://www.mathisfunforum.com/viewtopic … 00#p243200

Any ideas since then?

See you a little later, chore came up.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

I did not spend much time on the problem after that, let me see whether I can get anything else this time.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,656

Hi gAr;

Okay, thanks I am looking at it also.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,016

looks like a nice upper bound to start with.

*Last edited by anonimnystefy (2013-07-29 13:55:32)*

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: 105,656

Hi;

Upper and lower bounds imply some method of getting them. How?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 553

Hello,

gAr and bobbym those are the correct answers.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,656

Hi;

Thanks for the problem.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 553

Hello:

How many Lucky Numbers are there and show 3 ways to find them?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,656

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 553

Hello m:

I could use a bit of help on some M code.

Why do you call it Spasmatica?

Where does the integral come from? How can I evaluate it to many digits?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,656

I do not always call it that. Sometimes it is Asthmatica as well as some more colorful names.

Everything came from the Lando lectures.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 553

What are the Lando lectures?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,656

Lectures on Generating Functions by Lando, it is a book. I thought you had read it.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 553

I have that one.

How do you get the integral to say a hundred digits?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,656

I have that one.

Yes I know. I gave it to you. You might try reading it.

M can handle the integral exactly. You do not need an approximate answer.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 553

Oooh yes, I am sorry. It didn't work for me at first. The integral comes from complex analysis? From getting a0 of the Laurent series?

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

I was thinking about the integral you wrote there, I had

I got the first two answers using the g.f

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,656

It is straight out of the book. It does get the right answer. The derivation is a bit too tough for me.

What did you think of the NCR answer?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

nCr answer is derived from the g.f:

[z^27] in

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 553

Hello gAr;

That is good but it can also be derived from the principle of inclusion and exclusion.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,656

Hi;

I can follow gAr's better than that stuff on PIE. Did you understand it?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi ElainaVW,

I usually get PIE answers wrong, so I try to stay away from it!

When it's the case that g.f. is possible, I go for that.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,656

That is the way I feel about it too. I have a done a few of them but prefer generating functions.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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