Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#26 2013-02-03 04:21:32

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Kummer and a tough integral.

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


“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

Offline

#27 2013-02-03 04:24:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Kummer and a tough integral.

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


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.

Offline

#28 2013-02-03 04:27:42

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Kummer and a tough integral.

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


“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

Offline

#29 2013-02-03 04:30:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Kummer and a tough integral.

Oh brother, I am doing the wrong problem. You said t=x+n*2pi and I am doing t=x*n*2pi


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.

Offline

#30 2013-02-03 04:37:00

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Kummer and a tough integral.

Yes. t=x+2pi*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

Offline

#31 2013-02-03 04:37:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Kummer and a tough integral.

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


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.

Offline

#32 2013-02-03 05:23:30

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Kummer and a tough integral.

Great! So, do you think you will be able to expand it to 1000 digits with that?


“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

Offline

#33 2013-02-03 07:29:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Kummer and a tough integral.

Hi;

Nope, objection 2 and 3 still apply.


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.

Offline

#34 2013-02-03 08:36:47

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Kummer and a tough integral.

Have you found any other ways?


“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

Offline

#35 2013-02-03 08:44:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Kummer and a tough integral.

Nothing that could exceed about 100 digits. I used my idea with a few more bells and whistles.


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.

Offline

#36 2013-02-03 10:48:26

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Kummer and a tough integral.

Have you had other propositions about finding more digits?


“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

Offline

#37 2013-02-03 11:02:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Kummer and a tough integral.

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


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.

Offline

#38 2013-02-03 11:32:22

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Kummer and a tough integral.

Have you had other propositions about finding more digits?


“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

Offline

#39 2013-02-03 11:44:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Kummer and a tough integral.

Other problems like this one?


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.

Offline

#40 2013-02-03 12:01:29

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Kummer and a tough integral.

No. Did anyone tell you of another way to solve the integral problem?


“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

Offline

#41 2013-02-03 12:04:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Kummer and a tough integral.

I am afraid 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.

Offline

#42 2013-02-03 12:51:16

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Kummer and a tough integral.

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


“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

Offline

#43 2013-02-03 13:06:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Kummer and a tough integral.

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


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.

Offline

#44 2013-02-03 13:10:00

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Kummer and a tough integral.

Great then!


“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

Offline

#45 2013-03-04 06:33:09

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Kummer and a tough integral.

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?


“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

Offline

#46 2013-03-04 06:38:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Kummer and a tough integral.

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


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.

Offline

#47 2013-03-04 06:48:43

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Kummer and a tough integral.

I don't think there is anything built in.


“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

Offline

#48 2013-03-04 06:55:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Kummer and a tough integral.

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)


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.

Offline

#49 2013-03-04 07:04:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Kummer and a tough integral.

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


“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

Offline

#50 2013-03-04 07:07:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Kummer and a tough integral.

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

Board footer

Powered by FluxBB