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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,605

That is not correct. With respect to t, 2pi*n is a constant, so it vanishes. You should have dt=dx.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

It does not vanish, multiplicative constants go to the front.

t = 2 n π x

dt/dx = 2 n π

dt = 2 n π dx

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,605

You do not multiply x by it. You add it to x!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Oh brother, I am doing the wrong problem. You said t=x+n*2pi and I am doing t=x*n*2pi

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,605

Yes. t=x+2pi*n.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Okay thank you, I think I understand what he did there now.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Great! So, do you think you will be able to expand it to 1000 digits with that?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Hi;

Nope, objection 2 and 3 still apply.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,605

Have you found any other ways?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Nothing that could exceed about 100 digits. I used my idea with a few more bells and whistles.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,605

Have you had other propositions about finding more digits?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

I am not following you. Propositions? Do you mean other ideas?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,605

Have you had other propositions about finding more digits?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Other problems like this one?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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No. Did anyone tell you of another way to solve the integral problem?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

I am afraid not.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,605

Too bad. Be sure to tell me if you find something new.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

If I were to find something new I would tell immediately but every new idea just evaporates.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,605

Great then!

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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bobbym wrote:

To start, although any CAS known will gag on this problem they are able to do pieces of so it is to our advantage to split the integral like this.

The first integral is not too difficult and any CAS can do it to 100 digits.

Hi bobbym

I wanted to ask you about this bit. How do I get Maxima to evaluate this?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

What does maxima provide for numeric integration that is built in?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I don't think there is anything built in.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

There are numeric integration routines I think they are call quad_gags.

Also there is romberg and nint.

*Last edited by bobbym (2013-03-04 07:02:50)*

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,605

I tried loading nint, but it won't load!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Does this run?

```
(%i1) f(x) := (mode_declare (n, integer, x, float), n:n+1, exp(-x))$
(%i2) translate(f)$
Warning-> n is an undefined global variable.
(%i3) block ([rombergtol: 1.e-6, romberabs: 0.0], n:0, romberg (f, 0, 50));
(%o3) 1.000000000488271
(%i4) n;
(%o4) 257
```

**In mathematics, you don't understand things. You just get used to them.**

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