A257406 Decimal expansion of Integral_{0..infinity} log(x)/cosh(x) dx (negated).

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

Offset: 0

Author

Jean-François Alcover, Apr 22 2015

Keywords

• nonn
• cons
• easy

Examples

			-0.5208856126019768910801877375794544390636383554462853499753755842...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Victor Adamchik, A Class of Logarithmic Integrals (1997) Proc. of ISSAC'97

Crossrefs

Cf. A068466, A115252.

Programs

Mathematica

RealDigits[(Pi/2)*Log[4*Pi^3/Gamma[1/4]^4], 10, 103] // First
RealDigits[Integrate[-Log[x]/Cosh[x],{x,0,\[Infinity]}],10,120][[1]] (* Harvey P. Dale, Feb 05 2025 *)

PARI

(Pi/2)*log(4*Pi^3/gamma(1/4)^4) \\ Michel Marcus, Apr 22 2015

Formula

(Pi/2)*log(4*Pi^3/Gamma(1/4)^4).

Also equals 2*Integral_{0..1} (1/(x^2+1))*log(log(1/x)) dx.

Also equals 2*Integral_{Pi/4..Pi/2} log(log(tan(x))) dx.