A261508 - OEIS

%I #19 Mar 08 2023 07:44:20

%S 6,0,0,4,7,1,1,1,6,6,8,6,2,2,5,4,4,4,7,7,6,1,0,6,0,8,1,3,3,6,6,3,7,5,

%T 2,8,5,4,6,1,8,0,7,6,6,8,2,9,5,9,8,0,1,3,2,8,9,3,0,8,1,5,4,1,3,0,8,6,

%U 0,4,3,3,7,2,0,7,3,4,8,5,5,4,0,2,3,9,3,8,2,5,1,9,4,6,5,6,6,7,7,5,7,3,3,5,8

%N Decimal expansion of -zeta'''(0).

%H Tom M. Apostol, <a href="https://doi.org/10.1090/S0025-5718-1985-0771044-5">Formulas for higher derivatives of the Riemann zeta function</a>, Mathematics of Computation 44 (1985), pp. 223-232.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/StieltjesConstants.html">Stieltjes Constants</a>

%e 6.004711166862254447761060813366375285461807668295980132893...

%p evalf(-Zeta(3, 0), 120);

%t RealDigits[3*Log[2*Pi]*StieltjesGamma[1] + 3*EulerGamma*StieltjesGamma[1] + 3/2*StieltjesGamma[2] - Zeta[3] - 1/2*Log[2*Pi]^3 - 1/8*Pi^2*Log[2*Pi] + 3/2*EulerGamma^2*Log[2*Pi] + EulerGamma^3, 10, 120][[1]]

%o (PARI) -zeta'''(0) \\ _Charles R Greathouse IV_, Mar 10 2016

%Y Cf. A075700, A257549, A201995, A082633, A086279.

%K nonn,cons

%O 1,1

%A _Vaclav Kotesovec_, Aug 22 2015