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

Hmmm, I could not numerically integrate a function involving complex numbers.

"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: 94,477

Hi gAr;

I think you can in two ways.

1) Sage, Maxima and Wolfram can.

2) Any Newton-Coates formula is just a plug in, so complex numbers are no problem. Remember the answer was in complex 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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

I still can't do it. Sage demands a real number.

"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: 94,477

Hi gAr;

Okay, it isn't my preferred way of doing it either. Just interesting to see it work.

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

Hi bobbym,

Okay.

Did it work for large coefficients?

"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: 94,477

Hi gAr;

Yes, but then it becomes a difficult numerical problem.

Was the method I showed in the first post clear enough? Any CAS should be able to do that.

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

Hi bobbym,

Yes, the integral is good!

But I'm not very clear how it got converted to 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: 94,477

Hi gAr;

I am not following you, I meant post #1.

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

Oh, okay.

I was talking about #23.

"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: 94,477

Oh heck, do not worry about that. That is a big mystery to me. How could an integral with complex values zero in on one single coefficient?

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

Yes, a mystery!

That asymptotic form is also mysterious to me.

Can we directly expand about 0 and fit a polynomial?

"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: 94,477

Hi;

If you expand g(x) around 0 you will have a polynomial, the Taylor polynomial. Trying to truncate that by fitting a smaller polynomial should not work.

In A eq B there is theorem that says the principal part of the Laurents series expansion of g(x) is a good approximation of the coefficients of g(x). That is what I used.

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

Hi,

Okay, I'll check the book.

Thanks.

"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: 94,477

Hi;

Very good! You can help me out with it!

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

Gee, you're kidding again!

"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: 94,477

No kidding! I only get pieces of that book. I am amazingly stupid!

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

Hmmm, we'll see.

I am amazingly stupid!

You're not, otherwise you'd have ruled the nation!

"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: 94,477

Yikes, that is worse! I am not even the best at being an imbecile! I am mediocre!

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

Okay, now I get the estimate!

"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: 94,477

You got it! Very good. A book showed me a short cut over what I do but I do not remember what it was.

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

Okay.

I guess I have left too much of the book last time I read. I don't remember reading the book at all.

"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: 94,477

I found it kind of difficult and hard to piece together their algorithms. But it did give me the Hayman method and this method.

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

It's kind of frustrating to read such books.

We'll be dilemma whether to try to read again or skip it, whether the later parts depend on that etc.

"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: 94,477

Books like that should have more examples, a lot more. Math books should be all examples. I was recently looking through an article where the guy was apologizing for explaining his discoveries by examples! The other guys should be apologizing!

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

...the guy was apologizing for explaining his discoveries by examples!

That's funny!

Yes, you are right.

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

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