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

Author

Iaroslav V. Blagouchine, Mar 15 2015

Keywords

• nonn
• cons

Examples

			-0.0628164798060389979401584300937601437351823286924336...
		

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

Crossrefs

A115252 (first Malmsten integral), A256127 (second Malmsten integral), A256128 (third Malmsten integral), A002162 (log 2), A053510 (log Pi), A001620 (Euler's constant, gamma).

Programs

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 *)

PARI

(-Euler+log(Pi)-log(2))/2 \\ Michel Marcus, Mar 18 2015

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.