#15846: Incorrect series expansion of zeta(s) at 1
-------------------------------+------------------------
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:
-------------------------------+------------------------
Description changed by behackl:
Old description:
> {{{
> sage: zeta(x).series(x==1,2)
> (Infinity) + (zetaderiv(1, 1))*(x - 1) + Order((x - 1)^2)
> }}}
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*(-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.)
--
--
Ticket URL: <http://trac.sagemath.org/ticket/15846#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.