cp's OEIS Frontend

A257549 Decimal expansion of zeta''(0) (negated).

%I A257549 #27 Feb 16 2025 08:33:25
%S A257549 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,
%T A257549 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,
%U A257549 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
%N A257549 Decimal expansion of zeta''(0) (negated).
%C A257549 Essentially the same as A245273. - _R. J. Mathar_, Apr 30 2015
%H A257549 Tom M. Apostol, <a href="http://www.ams.org/journals/mcom/1985-44-169/S0025-5718-1985-0771044-5/">Formulas for higher derivatives of the Riemann zeta function</a>, Mathematics of Computation 44 (1985), p. 223-232.
%H A257549 Richard E. Crandall, <a href="http://marvinrayburns.com/UniversalTOC25.pdf">Unified algorithms for polylogarithm, L-series, and zeta variants.</a> p. 15.
%H A257549 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 104.
%H A257549 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>.
%H A257549 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StieltjesConstants.html">Stieltjes Constants</a>.
%F A257549 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.
%e A257549 2.00635645590858485121010002672996043819899491016091988116986828...
%p A257549 evalf(-Zeta(2, 0), 120); # _Vaclav Kotesovec_, Apr 29 2015
%t A257549 RealDigits[ StieltjesGamma[1] + EulerGamma^2/2 - Pi^2/24 - (1/2)*(Log[2] + Log[Pi])^2, 10, 104] // First
%o A257549 (PARI) -zeta''(0) \\ _Charles R Greathouse IV_, Mar 10 2016
%Y A257549 Cf. A075700, A082633, A261508, A201994.
%K A257549 nonn,cons,easy
%O A257549 1,1
%A A257549 _Jean-François Alcover_, Apr 29 2015