Re: Euler product

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

* Karim Belabas [2004-05-03 17:11]:
> * old [2004-05-03 12:08]:
> > Here is the constants I want to compute:
> > 
> > C(h)=prodeuler(p=2,infinity, (1+(1+1/p)^h/(p-1))/(1+(1+1/p)^(h-1)/(p-1)))
> > 
> > and with h quite large (up to 50).
> > 
> > I have a prodeulerrat by Henri Cohen, but the results are incoherent
>
> Looks like prodeulerrat uses heuristic bounds to evaluate the required
> accuracy. Catastrophic cancellation occured and was hidden away by the
> subsequent precision(res, pr), which added meaninless trailing zeroes to
> the result.
> 
> Try the attached variant, it should be slightly slower, but much safer
> [ also includes sumeulerrat() ].

As Olivier pointed out by private email, there was an off-by-1 error in the
attached file (one could get a "non existent component in truecoeff" error).

I have updated the "Contributed Scripts" page 

      http://www.math.u-psud.fr/~belabas/pari/scripts/

with a corrected script. So, please use

      http://www.math.u-psud.fr/~belabas/pari/scripts/cohen.gp

instead.

Cheers,

    Karim.
-- 
Karim Belabas                     Tel: (+33) (0)1 69 15 57 48
Dep. de Mathematiques, Bat. 425   Fax: (+33) (0)1 69 15 60 19
Universite Paris-Sud              http://www.math.u-psud.fr/~belabas/ 
F-91405 Orsay (France)            http://pari.math.u-bordeaux.fr/  [PARI/GP]