Changes between Initial Version and Version 1 of Ticket #21899
- Timestamp:
- 11/19/16 10:09:14 (4 years ago)
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Ticket #21899 – Description
initial v1 3 3 zeta function around s=1 is 4 4 5 {{{ 5 6 zeta(s) = 1/(s-1) + gamma_0 - gamma_1 (s-1) + O((s-1)^2). 7 }}} 6 8 7 9 However, sage says 8 10 11 {{{ 9 12 sage: zeta(s).series(s==1, 2) 10 13 1*(s - 1)^(-1) + (euler_gamma) + (-1/2*stieltjes(1))*(s - 1) + Order((s - 1)^2) 11 14 }}} 12 15 (note the denominator 2 in the coefficient of (s-1)). 13 16 14 17 Numerically, 15 18 19 {{{ 16 20 sage: stieltjes(1.) 17 21 -0.0728158454836767 18 22 }}} 19 23 and Wikipedia states that 20 24 25 {{{ 21 26 gamma_1 = −0.0728158454836767248605863758749013191377363383 ... 27 }}} 22 28 23 29 It seems that there is an incorrect factor in sage.