Changes between Initial Version and Version 1 of Ticket #21899


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Timestamp:
11/19/16 10:09:14 (4 years ago)
Author:
cheuberg
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  • Ticket #21899 – Description

    initial v1  
    33zeta function around s=1 is
    44
     5{{{
    56zeta(s) = 1/(s-1) + gamma_0 - gamma_1 (s-1) + O((s-1)^2).
     7}}}
    68
    79However, sage says
    810
     11{{{
    912sage: zeta(s).series(s==1, 2)
    10131*(s - 1)^(-1) + (euler_gamma) + (-1/2*stieltjes(1))*(s - 1) + Order((s - 1)^2)
    11 
     14}}}
    1215(note the denominator 2 in the coefficient of (s-1)).
    1316
    1417Numerically,
    1518
     19{{{
    1620sage: stieltjes(1.)
    1721-0.0728158454836767
    18 
     22}}}
    1923and Wikipedia states that
    2024
     25{{{
    2126gamma_1 = −0.0728158454836767248605863758749013191377363383      ...
     27}}}
    2228
    2329It seems that there is an incorrect factor in sage.