---------- Forwarded message ----------
From: Robert Pollak <[email protected]>
Date: 29 October 2014 08:40
Subject: Re: Two new formulas for zeta(3)
To: [email protected]
Dear Zhi-Wei Sun,
you wrote on 2014-10-24:
> zeta(3) = Sum_{k>0} (3*H(k)-1/k)/(k^2*binom(2k,k)). (1)
>
> Via the Mathematica command
>
> FullSimplify[Sum[(3*HarmonicNumber[k]-1/k)/(k^2*Binomial[2k,k]),{k,1,Infinity}]],
>
> Mathematica 9 could yield the desired result zeta(3) half an hour later.
> So, (1) does have a proof.
I agree that this Mathematica result is a strong hint that (1) holds -
but I would not call it a proof: I guess that in Mathematica there is
no way to access all computation steps, s.t. the calculation can be
checked (e.g. with other software). Or is there? Is there at least a
list of the main computation steps available?
I am not a number theorist, so let me ask: Is there any open source
software that one could use to check this formula?
Best regards,
Robert Pollak
Disclaimer: I have found your posting via the thread "Can We Trust
Computer Algebra Systems?" on the sage-devel list.
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