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#1 2011-08-19 01:20:39

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

Riemann zeta function and Harmonic number

A result due to Euler


Hence, we have

etc...


"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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#2 2011-08-19 02:25:39

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

Re: Riemann zeta function and Harmonic number

Hello gAr;

Very nice!


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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#3 2011-08-19 02:40:18

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

Re: Riemann zeta function and Harmonic number

Hi bobbym,

Yes!
Couldn't find a proof though.


"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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#4 2011-08-19 03:04:36

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

Re: Riemann zeta function and Harmonic number

Hi gAr;

Here is some mind boggling stuff that uses the hyperharmonic numbers. The harmonic number is a subset of them.

http://www.inf.unideb.hu/valseg/dolgozo … rhsums.pdf


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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#5 2011-08-19 03:19:07

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

Re: Riemann zeta function and Harmonic number

Hi bobbym,

That's awesome stuff!
It cited a reference which has the idea to prove the identity: http://algo.inria.fr/flajolet/Publications/FlSa98.pdf

Need time to understand, if I'm able to!

Thanks.


"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."

Offline

#6 2011-08-19 04:38:34

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

Re: Riemann zeta function and Harmonic number

Hi gAr;

Your welcome!


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

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