A102047 Decimal expansion of -1/4 + log(2)/2.

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

Offset: 0

Author

Eric W. Weisstein, Dec 26 2004

Keywords

• nonn
• cons

Examples

			-1/4 + log(2)/2 = 0.0965735902...
		

Links

• Eric Weisstein's World of Mathematics, Abel's Integral.
• Eric Weisstein's World of Mathematics, Cosine Integral.
• Index entries for transcendental numbers

Crossrefs

Cf. A016655.

Programs

Mathematica

RealDigits[Log[2]/2 - 1/4, 10, 100][[1]] (* Amiram Eldar, Sep 08 2020 *)

PARI

log(2)/2 - 1/4 \\ Charles R Greathouse IV, May 15 2019

Formula

Equals A016655/10 - 1/4. - R. J. Mathar, Dec 13 2008

From Amiram Eldar, Sep 08 2020: (Start)

Equals Sum_{k>=1} (-1)^(k+1)/((2*k+1)^2-1).

Equals Sum_{k>=1} Ci((2*k-1)*Pi), where Ci(x) is the cosine integral.

Equals Integral_{x=1..oo} log(x)/(x+1)^3 dx. (End)