A324021 - OEIS

%I #14 Nov 02 2023 10:40:48

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

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

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

%N Decimal expansion of integral_{x>0} tanh(x)^3/x^2 dx.

%H Igor Khavkine, <a href="https://mathoverflow.net/questions/271526">Is there a closed form for integral_{x>0} tanh(x)^3/x^2 dx</a>, MathOverflow, 2017.

%H Jing Li and Wenchang Chu, <a href="https://arxiv.org/abs/2310.19847">Integrals of Hyperbolic Tangent Function</a>, arXiv:2310.19847 [math.GM], 2023. Has similar integrals.

%F 5/6 - gamma - 19*log(2)/15 + 12*log(A) - log(Pi) + 90*zeta'(4)/Pi^4, where gamma is the Euler-Mascheroni constant, and A is the Glaisher constant.

%e 1.15478531332317626405907045194152614753523709245089248909911022029...

%t RealDigits[N[5/6 - EulerGamma - 19 Log[2]/15 + 12 Log[Glaisher] - Log[Pi] + 90 Zeta'[4]/Pi^4, 101]][[1]]

%Y Cf. A074962 (Glaisher constant), A261506 (-zeta'(4)).

%K nonn,cons

%O 1,3

%A _Jean-François Alcover_, Sep 01 2019