OFFSET
0,1
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 + x^2) dx.
Equals integral_{x=0..infinity} log(x)/(1 - 2*cosh(x)) dx.
Equals Pi*(7*log(2) + 8*log(Pi) - 3*log(3) - 12*log(Gamma(1/3)))/(3*sqrt(3)).
EXAMPLE
-0.671719601885874542354405069288779884008802066219356...
MAPLE
evalf(Pi*(7*log(2)+8*log(Pi)-3*log(3)-12*log(GAMMA(1/3)))/(3*sqrt(3)), 120); # Vaclav Kotesovec, Mar 17 2015
MATHEMATICA
RealDigits[Pi*(7*Log[2]+8*Log[Pi]-3*Log[3]-12*Log[Gamma[1/3]])/(3*Sqrt[3]), 10, 105][[1]] (* Vaclav Kotesovec, Mar 17 2015 *)
PROG
(PARI) Pi*(7*log(2)+8*log(Pi)-3*log(3)-12*log(gamma(1/3)))/(3*sqrt(3)) \\ Michel Marcus, Mar 18 2015
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Iaroslav V. Blagouchine, Mar 15 2015
STATUS
approved