Re: Precision loss of zeta(2)-zetahurwitz(2,N+1) in some range of N ?

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* Gottfried Helms [2021-12-23 08:35]:
> I recently came across this, when I wanted to
> use zeta and zetahurwitz for sum of reciprocal squares
> up to large N. My default precision is always 200 dec
> digits and so this gave a signal... (I never
> observed such a problem of loss of precision with the
> harmonic numbers and the psi()-function)
> 
> H2o(m)=sum(k=1,m,1.0/k^2)
> H2(m)=zeta(2)-zetahurwitz(2,m+1)
> 
> H2o(20)-H2(20)
> H2o(200)-H2(200)
> H2o(2000)-H2(2000)
> H2o(20000)-H2(20000)
> H2o(200000)-H2(200000)

The(trivial) case Re(s) >= 0 and x >> 1 was treated incorrectly.
It's now fixed in 'master'.

Thanks for your report !

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
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