Math Is Fun Forum

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Riemann zeta function and Harmonic number

A result due to Euler

Hence, we have

etc...

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"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Riemann zeta function and Harmonic number

Hello gAr;

Very nice!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Riemann zeta function and Harmonic number

Hi gAr;

Your welcome!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.