id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
21899,Document Stieltjes constants,cheuberg,,"According to https://en.wikipedia.org/wiki/Stieltjes_constants as well as
to http://dlmf.nist.gov/25.2.E4, the Laurent series expansion of the Riemann
zeta function around s=1 is
{{{
zeta(s) = 1/(s-1) + gamma_0 - gamma_1 (s-1) + O((s-1)^2).
}}}
However, sage says
{{{
sage: zeta(s).series(s==1, 2)
1*(s - 1)^(-1) + (euler_gamma) + (-1/2*stieltjes(1))*(s - 1) + Order((s - 1)^2)
}}}
(note the denominator 2 in the coefficient of (s-1)).
Numerically,
{{{
sage: stieltjes(1.)
-0.0728158454836767
}}}
and Wikipedia states that
{{{
gamma_1 = −0.0728158454836767248605863758749013191377363383 ...
}}}
It seems that there is an incorrect factor in sage (this is now fixed and doctested).
When fixing this, the documentation of stieltjes should be improved to actually contain a definition of the stieltjes constants instead of simply stating that ""The Stieltjes constants are used in the series expansions of zeta(s).""
",enhancement,new,minor,sage-7.5,symbolics,,,behackl,,,,N/A,,,,#21855,