A102047 - OEIS

%I #16 Sep 08 2020 06:15:36

%S 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,

%T 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,

%U 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

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AbelsIntegral.html">Abel's Integral</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CosineIntegral.html">Cosine Integral</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals A016655/10 - 1/4. - _R. J. Mathar_, Dec 13 2008

%F From _Amiram Eldar_, Sep 08 2020: (Start)

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

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

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

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

%t RealDigits[Log[2]/2 - 1/4, 10, 100][[1]] (* _Amiram Eldar_, Sep 08 2020 *)

%o (PARI) log(2)/2 - 1/4 \\ _Charles R Greathouse IV_, May 15 2019

%Y Cf. A016655.

%K nonn,cons

%O 0,2

%A _Eric W. Weisstein_, Dec 26 2004