[seqfan] Re: Wrong formula in Wolfram functions

[Georgi Guninski]

On Sat, Mar 31, 2012 at 04:01:07PM +0200, Wouter Meeussen wrote:
> Enrique, funny:
> 
> my version 4.1 gives it correctly as
> Sum[MoebiusMu[k]^2/k^s, {k, 1, Infinity}]  ==> Zeta[s]/Zeta[2s]
> 
> but then it garbles this one:
> Sum[ EulerPhi[k]/k^s, {k, 1,Infinity}]  =/=> Zeta[-1 + s] Zeta[s]
> should be  Zeta[-1 + s] / Zeta[s]
> 
> New Versions? hmm,
> "plus ça change, plus ça reste la même chose"?
> or: "you can prove the presence of bugs, but never the absence of'm"
> 
> Wouter.
> 
>

Are these sums hardcoded as axioms or proved/found by the software?