A256129 Decimal expansion of the fourth Malmsten integral: int_{x=1..infinity} log(log(x))/(1 + x)^2 dx, negated.

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

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