|
|
A256128
|
|
Decimal expansion of the third Malmsten integral: int_{x=1..infinity} log(log(x))/(1 - x + x^2) dx, negated.
|
|
6
|
|
|
6, 7, 1, 7, 1, 9, 6, 0, 1, 8, 8, 5, 8, 7, 4, 5, 4, 2, 3, 5, 4, 4, 0, 5, 0, 6, 9, 2, 8, 8, 7, 7, 9, 8, 8, 4, 0, 0, 8, 8, 0, 2, 0, 6, 6, 2, 1, 9, 3, 5, 6, 3, 3, 2, 0, 5, 3, 6, 1, 6, 7, 3, 3, 7, 5, 1, 2, 5, 1, 2, 1, 7, 1, 7, 5, 8, 6, 1, 9, 0, 2, 1, 8, 3, 2, 6, 7, 1, 2, 6, 8, 6, 2, 9, 3, 2, 3, 7, 2, 3, 5, 5, 0, 3, 6
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
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
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|