#15846: Incorrect series expansion of zeta(s) at 1
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Reporter: mmezzarobba | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Old description:
> The series expansion of the zeta function around its singularity at `s=1`
> is incorrect. Within Sage, we have
>
> {{{
> sage: zeta(x).series(x==1,2)
> (Infinity) + (zetaderiv(1, 1))*(x - 1) + Order((x - 1)^2)
> }}}
>
> when in fact, we should have
>
> {{{
> sage: zeta(x).series(x==1, 1)
> 1*(-1+x)^(-1)+(log(pi)+log(2)+euler_gamma+2*zetaderiv(1,0))+Order(-1+x)
> }}}
>
> (see http://dlmf.nist.gov/25.2.E4 for the expansion like it is supposed
> to be.)
New description:
The series expansion of the zeta function around its singularity at `s=1`
is incorrect. Within Sage, we have
{{{
sage: zeta(x).series(x==1,2)
(Infinity) + (zetaderiv(1, 1))*(x - 1) + Order((x - 1)^2)
}}}
when in fact, we should have
{{{
sage: zeta(x).series(x==1, 1)
1*(x - 1)^(-1) + (euler_gamma + log(2) + log(pi) + 2*zetaderiv(1, 0)) +
Order(x - 1)
}}}
(see http://dlmf.nist.gov/25.2.E4 for the expansion like it is supposed to
be.)
--
Comment (by behackl):
I just compiled sage with the patch added to pynac, and now I get
{{{
sage: zeta(x).series(x==1, 1)
1*(x - 1)^(-1) + (euler_gamma + log(2) + log(pi) + 2*zetaderiv(1, 0)) +
Order(x - 1)
}}}
Seems to work. :-)
So, in order to get this ticket resolved and have the fix in Sage, what is
the best way to proceed from here? I'd certainly like to commit the
changes to your github mirror -- but what happens then?
Replying to [comment:11 rws]:
> > I do not have the impression that Pynac has ever upgraded its GiNaC
part since the point in time the fork was made.
> Ah okay, I thought you made a patch on top of The Official GiNaC, i.e.,
http://www.ginac.de/ginac.git/
Well, as of yet I have done nothing, really (except for fixing this thing
locally). ;-)
But I guess I could also submit my changes there, the official GiNaC
version also has the same problem w.r.t. the expansion of zeta. (However,
the version on git wouldn't compile for me yesterday, so for fixing this I
initially used the tarball on their website...)
--
Ticket URL: <http://trac.sagemath.org/ticket/15846#comment:12>
Sage <http://www.sagemath.org>
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