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

0,2

Links

Table of n, a(n) for n=0..102.

Eric Weisstein's World of Mathematics, Abel's Integral.

Eric Weisstein's World of Mathematics, Cosine Integral.

Index entries for transcendental numbers

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)

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A016655.

Sequence in context: A367709 A247040 A019942 * A144665 A019884 A103814

Adjacent sequences: A102044 A102045 A102046 * A102048 A102049 A102050

Keyword

nonn,cons

Author

Eric W. Weisstein, Dec 26 2004

Status

approved