A257549 Decimal expansion of zeta''(0) (negated).
2, 0, 0, 6, 3, 5, 6, 4, 5, 5, 9, 0, 8, 5, 8, 4, 8, 5, 1, 2, 1, 0, 1, 0, 0, 0, 2, 6, 7, 2, 9, 9, 6, 0, 4, 3, 8, 1, 9, 8, 9, 9, 4, 9, 1, 0, 1, 6, 0, 9, 1, 9, 8, 8, 1, 1, 6, 9, 8, 6, 8, 2, 8, 0, 8, 5, 7, 7, 6, 0, 0, 7, 8, 3, 9, 8, 0, 8, 5, 3, 4, 2, 7, 6, 4, 8, 7, 0, 5, 6, 0, 3, 2, 8, 0, 8, 3, 9, 2, 4, 7, 2, 6, 6
Offset: 1
Examples
2.00635645590858485121010002672996043819899491016091988116986828...
Links
- Tom M. Apostol, Formulas for higher derivatives of the Riemann zeta function, Mathematics of Computation 44 (1985), p. 223-232.
- Richard E. Crandall, Unified algorithms for polylogarithm, L-series, and zeta variants. p. 15.
- Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 104.
- Eric Weisstein's World of Mathematics, Riemann Zeta Function.
- Eric Weisstein's World of Mathematics, Stieltjes Constants.
Programs
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Maple
evalf(-Zeta(2, 0), 120); # Vaclav Kotesovec, Apr 29 2015
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Mathematica
RealDigits[ StieltjesGamma[1] + EulerGamma^2/2 - Pi^2/24 - (1/2)*(Log[2] + Log[Pi])^2, 10, 104] // First
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PARI
-zeta''(0) \\ Charles R Greathouse IV, Mar 10 2016
Formula
zeta''(0) = gamma_1 + gamma^2/2 - Pi^2/24 - (1/2)*(log(2)+log(Pi))^2, where gamma_1 is the first Stieltjes constant.
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