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 A256129 Decimal expansion of the fourth Malmsten integral: int_{x=1..infinity} log(log(x))/(1 + x)^2 dx, negated. 5
 0, 6, 2, 8, 1, 6, 4, 7, 9, 8, 0, 6, 0, 3, 8, 9, 9, 7, 9, 4, 0, 1, 5, 8, 4, 3, 0, 0, 9, 3, 7, 6, 0, 1, 4, 3, 7, 3, 5, 1, 8, 2, 3, 2, 8, 6, 9, 2, 4, 3, 3, 6, 4, 0, 7, 0, 6, 4, 1, 2, 0, 8, 6, 4, 5, 3, 0, 6, 1, 7, 8, 9, 4, 3, 1, 2, 6, 6, 6, 5, 3, 3, 7, 9, 5, 9, 3, 5, 6, 0, 0, 0, 6, 3, 3, 7, 8, 6, 4, 6, 7, 7, 3, 1, 1, 5, 5, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 Iaroslav V. Blagouchine, Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results, The Ramanujan Journal, Volume 35, Issue 1, pp. 21-110, 2014, DOI: 10.1007/s11139-013-9528-5. PDF file Wikipedia, Carl Malmsten FORMULA Equals integral_{x=0..1} log(log(1/x))/(1 + x)^2 dx. Equals integral_{x=0..infinity} 0.5*log(x)/(1 + cosh(x)) dx. Equals (log(Pi) - log(2) - gamma)/2. EXAMPLE -0.0628164798060389979401584300937601437351823286924336... MAPLE evalf((log(Pi/2)-gamma)/2, 120); # Vaclav Kotesovec, Mar 17 2015 MATHEMATICA RealDigits[(Log[Pi/2]-EulerGamma)/2, 10, 105][[1]] (* Vaclav Kotesovec, Mar 17 2015 *) PROG (PARI) (-Euler+log(Pi)-log(2))/2 \\ Michel Marcus, Mar 18 2015 CROSSREFS A115252 (first Malmsten integral), A256127 (second Malmsten integral), A256128 (third Malmsten integral), A002162 (log 2), A053510 (log Pi), A001620 (Euler's constant, gamma). Sequence in context: A177889 A086744 A242301 * A019692 A031259 A059629 Adjacent sequences:  A256126 A256127 A256128 * A256130 A256131 A256132 KEYWORD nonn,cons AUTHOR Iaroslav V. Blagouchine, Mar 15 2015 STATUS approved

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Last modified March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)