A324021 Decimal expansion of integral_{x>0} tanh(x)^3/x^2 dx.

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, 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, 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

Offset

1,3

Links

Table of n, a(n) for n=1..101.

Igor Khavkine, Is there a closed form for integral_{x>0} tanh(x)^3/x^2 dx, MathOverflow, 2017.

Jing Li and Wenchang Chu, Integrals of Hyperbolic Tangent Function, arXiv:2310.19847 [math.GM], 2023. Has similar integrals.

Formula

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.

Example

1.15478531332317626405907045194152614753523709245089248909911022029...

Mathematica

RealDigits[N[5/6 - EulerGamma - 19 Log[2]/15 + 12 Log[Glaisher] - Log[Pi] + 90 Zeta'[4]/Pi^4, 101]][[1]]

Crossrefs

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

Sequence in context: A103549 A011285 A111421 * A323983 A333203 A340705

Adjacent sequences: A324018 A324019 A324020 * A324022 A324023 A324024

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 01 2019

Status

approved