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A102047
Decimal expansion of -1/4 + log(2)/2.
1
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
Eric Weisstein's World of Mathematics, Abel's Integral.
Eric Weisstein's World of Mathematics, Cosine Integral.
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
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Dec 26 2004
STATUS
approved