|
|
A214550
|
|
Decimal expansion of Sum_{n>=0} 1/(3*n+1)^2.
|
|
8
|
|
|
1, 1, 2, 1, 7, 3, 3, 0, 1, 3, 9, 3, 6, 3, 4, 3, 7, 8, 6, 8, 6, 5, 7, 7, 8, 2, 3, 3, 3, 2, 1, 3, 9, 0, 7, 0, 6, 7, 2, 4, 3, 2, 2, 6, 7, 9, 9, 2, 0, 1, 0, 8, 6, 8, 2, 4, 3, 7, 9, 6, 4, 8, 0, 0, 0, 9, 2, 3, 3, 5, 7, 0, 1, 3, 9, 3, 8, 9, 8, 3, 8, 6, 3, 0, 5, 8, 2, 5, 4, 0, 7, 9, 1, 3, 7, 7, 5, 4, 6, 6, 2, 0, 1, 1, 8
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Sum over the inverse squares of A016777. Dirichlet series Sum_{n>=1} A079978(n-1)/n^s at s=2.
This is also (1/9)*Zeta(2, 1/3) = (1/9)*Psi(1, 1/3) with the Hurwitz zeta function Zeta(s, a) and the Polygamma function Psi(n, z). See the programs. - Wolfdieter Lang, Nov 12 2017
|
|
LINKS
|
|
|
FORMULA
|
Equals Integral_{0..1} log(x)/(x^3-1) dx = Integral_{1..oo} x*log(x)/(x^3-1) dx.
|
|
EXAMPLE
|
1.1217330139363437868657... = 1/1^2 + 1/4^2 + 1/7^2 + 1/10^2 + 1/13^2 + ...
|
|
MAPLE
|
evalf(Psi(1, 1/3)/9);
|
|
MATHEMATICA
|
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|