A372858 Decimal expansion of (1 + log(2))/2.

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

Offset: 0

Author

Clark Kimberling, Jun 09 2024

Keywords

• nonn
• cons

Examples

			0.84657359027997265470861606072908828403775006...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A019798, A372859, A372860, A372861.

Essentially the same as A016655, A102047.

Programs

Mathematica

s = Integrate[Log[x]/x^2, {x, 2, Infinity}]
d = N[s, 100]
First[RealDigits[d]]
N[1/2  (1 + Log[2]), 100]
RealDigits[(1+Log[2])/2,10,120][[1]] (* Harvey P. Dale, Aug 05 2025 *)

PARI

log(2)/2+.5 \\ Charles R Greathouse IV, Nov 21 2024

Formula

Equals Integral_{x=2..oo} (log(x))/x^2 dx.

Equals log(A019798). - Hugo Pfoertner, Jun 09 2024

Integral log(x)/x^m dx = -x^(1-m) Sum_{k=0..1} log^(1-k)(x)/(m-1)^(k+1). - R. J. Mathar, Jun 21 2024