|
|
A269768
|
|
Decimal expansion of Sum_{n>=2} (-1)^n * zeta(n)/n!.
|
|
2
|
|
|
6, 5, 9, 8, 1, 5, 2, 5, 4, 3, 4, 9, 9, 9, 9, 5, 1, 4, 8, 6, 3, 8, 4, 4, 1, 7, 4, 3, 5, 2, 9, 5, 8, 9, 9, 6, 0, 7, 7, 7, 7, 0, 0, 7, 4, 0, 8, 8, 8, 0, 8, 5, 4, 1, 3, 8, 4, 1, 2, 1, 3, 4, 9, 3, 2, 0, 6, 3, 3, 9, 8, 9, 0, 7, 5, 7, 3, 1, 6, 7, 8, 5, 1, 8, 5, 7, 6, 2, 4, 8, 3, 0, 0, 8, 7, 8, 6, 0, 9, 6, 0, 7, 5, 8, 0, 9
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
FORMULA
|
Equals Sum_{k>=1} (exp(-1/k) - 1 + 1/k).
Apparently equals 1/2 - Integral_{x=0..oo} (coth(Pi/x)*(sin(x)/x^2 - 1/x) + 1/Pi) dx.
The proposed expression is difficult to evaluate to arbitrary precision.
Maple code: evalf[50](1/2 - Int(coth(Pi/x)*(sin(x)/x^2 - 1/x) + 1/Pi, x = 0 .. infinity));
Mathematica code: 1/2-NIntegrate[Coth[Pi/t] (Sin[t]/t^2-1/t)+1/Pi,{t,0,Infinity},WorkingPrecision->50,MinRecursion->7]
(End)
|
|
EXAMPLE
|
0.659815254349999514863844174352958996077770074088808541384121349320633989...
|
|
MAPLE
|
evalf(Sum(exp(-1/n)-1+1/n, n=1..infinity), 120);
|
|
MATHEMATICA
|
RealDigits[NSum[Exp[-1/n] - 1 + 1/n, {n, 1, Infinity}, WorkingPrecision -> 200, NSumTerms -> 10000, PrecisionGoal -> 120, Method -> {"NIntegrate", "MaxRecursion" -> 100}]][[1]]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|