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.

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

gAr
Member
Registered: 2011-01-09
Posts: 3,462

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."

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,675

Re: Riemann zeta function and Harmonic number

Hello gAr;

Very nice!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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

gAr
Member
Registered: 2011-01-09
Posts: 3,462

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."

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,675

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

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

gAr
Member
Registered: 2011-01-09
Posts: 3,462

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: 81,675

Re: Riemann zeta function and Harmonic number

Hi gAr;

Your welcome!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

Board footer

Powered by FluxBB