A379425 Decimal expansion of Ni_2 = gamma/3 - log(2*Pi)/2 - 2*zeta'(-1) + 2/3, where gamma = A001620.
2, 7, 0, 9, 7, 5, 6, 4, 2, 4, 9, 6, 7, 4, 0, 0, 7, 0, 1, 8, 3, 0, 1, 3, 6, 1, 4, 1, 0, 7, 4, 1, 1, 1, 2, 2, 6, 8, 0, 7, 2, 8, 3, 9, 9, 0, 1, 2, 5, 9, 4, 6, 8, 7, 4, 5, 1, 1, 4, 8, 8, 1, 7, 1, 9, 3, 5, 7, 6, 2, 7, 8, 9, 9, 8, 4, 4, 8, 8, 3, 8, 1, 3, 6, 6, 2, 2, 5, 8, 9, 7, 9, 2, 9, 7, 8, 8, 9, 6, 6, 2, 6, 2, 9, 2
Offset: 0
Examples
0.270975642496740070183013614107411122680728399012594687451148817...
Links
- Marc-Antoine Coppo, A note on some alternating series involving zeta and multiple zeta values, Journal of Mathematical Analysis and Applications Volume 475, Issue 2, 15 July 2019, Pages 1831-1841.
Programs
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Mathematica
RealDigits[EulerGamma/3 - Log[2 Pi]/2 + 2/3 - 2 Zeta'[-1], 10, 105][[1]]