|
| |
|
|
A256127
|
|
Decimal expansion of the second Malmsten integral: Integer_{x >= 1} log(log(x))/(1 + x + x^2) dx, negated.
|
|
6
|
|
|
|
1, 2, 6, 3, 2, 1, 4, 8, 1, 7, 0, 6, 2, 0, 9, 0, 3, 6, 3, 6, 5, 2, 2, 6, 7, 5, 3, 2, 5, 3, 2, 0, 2, 3, 9, 1, 8, 4, 4, 2, 4, 4, 3, 0, 9, 4, 6, 5, 2, 8, 3, 5, 1, 6, 3, 7, 8, 9, 9, 7, 4, 3, 0, 4, 2, 9, 0, 8, 6, 7, 4, 0, 0, 8, 5, 1, 2, 5, 4, 3, 7, 1, 7, 8, 0, 5, 2, 9, 7, 4, 1, 9, 8, 2, 9, 7, 0, 0, 2, 2, 4, 8, 7, 6
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
|
|
|
FORMULA
|
Equals Integral_{x=0..1} log(log(1/x))/(1 + x + x^2) dx.
Equals Integral_{x>=0} log(x)/(1 + 2*cosh(x)) dx.
Equals Pi*(8*log(2*Pi) - 3*log(3) - 12*log(Gamma(1/3)))/(6*sqrt(3)).
|
|
|
EXAMPLE
|
-0.12632148170620903636522675325320239184424430946528...
|
|
|
MAPLE
|
evalf(Pi*(8*log(2*Pi) - 3*log(3) - 12*log(GAMMA(1/3)))/(6*sqrt(3)), 120); # Vaclav Kotesovec, Mar 17 2015
|
|
|
MATHEMATICA
|
RealDigits[Integrate[Log[Log[1/x]]/(1 + x + x^2), {x, 0, 1}], 10, 100][[1]] (* Alonso del Arte, Mar 16 2015 *)
RealDigits[Pi*(8*Log[2*Pi] - 3*Log[3] - 12*Log[Gamma[1/3]])/(6*Sqrt[3]), 10, 105][[1]] (* Vaclav Kotesovec, Mar 17 2015 *)
|
|
|
PROG
|
(PARI) Pi*(8*log(2*Pi) - 3*log(3) - 12*log(gamma(1/3)))/(6*sqrt(3)) \\ Michel Marcus, Mar 18 2015
(PARI) intnum(x=0, 1, log(log(1/x))/(1 + x + x^2))
(PARI) intnum(x=1, oo, log(log(x))/(1 + x + x^2))
(PARI) intnum(x=0, [oo, 1], log(x)/(1 + 2*cosh(x))) \\ Gheorghe Coserea, Sep 26 2018
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
