#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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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>
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