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#1951 2013-10-01 18:13:30

anonimnystefy
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Re: Is this cool with you?

How did you get 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

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#1952 2013-10-01 18:37:26

bobbym
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Re: Is this cool with you?

http://mathworld.wolfram.com/RiemannZetaFunction.html

Formula 19 - 20

But the important thing is why is it better?


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.

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#1953 2013-10-02 05:57:12

anonimnystefy
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Re: Is this cool with you?

Because it's alternating, of course. RRA is not working too fast, though. I cannot evaluate it quickly...


“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

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#1954 2013-10-02 09:35:33

bobbym
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From: Bumpkinland
Registered: 2009-04-12
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Re: Is this cool with you?

Alternating series can be hard to accelerate too! Heard of the converger?


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.

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#1955 2013-10-02 16:32:36

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,520

Re: Is this cool with you?

No. What is it?


“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

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#1956 2013-10-02 19:11:27

bobbym
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From: Bumpkinland
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Re: Is this cool with you?

acc[n_]:=Module[{d,b,c,s},
d=(3+Sqrt[8])^n;
d=(d+1/d)/2;
b=-1;
c=-d;
s=0;
Table[c=b-c;s=s+c*a[k];b=(k+n)(k-n) b/((k+1/2)(k+1)),{k,0,n-1}];
s/d]

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.

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#1957 2013-10-03 01:20:23

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,520

Re: Is this cool with you?

How does it work?


“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

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#1958 2013-10-03 02:21:58

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Is this cool with you?

I knew you were going to say that...


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.

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#1959 2013-10-03 02:29:26

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,520

Re: Is this cool with you?

And you do not know?


“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

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#1960 2013-10-03 02:34:26

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Is this cool with you?

I knew you were going to ask that.

First, it is for alternating series only. So enter

a[k_]:=1 / ( k + 1 ) then

N[acc[250],200]


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.

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#1961 2013-10-03 02:48:43

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,520

Re: Is this cool with you?

Hi

I am getting 0.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641868754200148102057068573368552023575813055703267075163507596193072757082837143519030703862389167347122161...


“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

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#1962 2013-10-03 02:50:10

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Is this cool with you?

Now enter:

N[Log[2],200]

what do you notice?


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.

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#1963 2013-10-03 02:53:48

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,520

Re: Is this cool with you?

Wow, 196 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

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#1964 2013-10-03 02:56:09

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Is this cool with you?

No what series you just did?


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.

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#1965 2013-10-03 03:04:46

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,520

Re: Is this cool with you?


“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

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#1966 2013-10-03 03:06:25

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Is this cool with you?

The converger always starts at 0.


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.

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#1967 2013-10-03 03:22:02

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,520

Re: Is this cool with you?

Same series.


“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

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#1968 2013-10-03 03:24:22

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Is this cool with you?

Yes, but it will affect what you enter into a[k_]


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.

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#1969 2013-10-03 03:58:23

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,520

Re: Is this cool with you?

That is true, but you asked what the series was.


“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

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#1970 2013-10-03 04:04:05

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Is this cool with you?

Yes, but I meant in the form that the converger can use.

1) The series must be alternating.

2) It must start at 0.

The function acc has an input and a global variable a. These must be in the precise form required. That is why I did the transformation on the zeta series.


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.

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#1971 2013-10-03 23:35:20

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,520

Re: Is this cool with you?

No, no, I got that it must start at 0. I was just saying that what I wrote and what you wrote are the same series.

So, you've got no idea how and why it works?


“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

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#1972 2013-10-04 01:41:09

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Is this cool with you?

None at all. Did you see how it works on zeta(3)?


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.

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#1973 2013-10-04 01:52:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,520

Re: Is this cool with you?

Haven't tried. I will do it tomorrow.

What is tthe algorithm based on?


“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

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#1974 2013-10-04 01:58:51

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,242

Re: Is this cool with you?

The converger? I do not know,


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.

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#1975 2013-10-04 21:24:14

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,520

Re: Is this cool with you?

Too bad.


“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

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