|
|
A086722
|
|
Decimal expansion of g(1)+g(2)-g(4)-g(5), where g(k) = Sum_{m>=0} (1/(6*m+k)^2).
|
|
11
|
|
|
1, 1, 7, 1, 9, 5, 3, 6, 1, 9, 3, 4, 4, 7, 2, 9, 4, 4, 5, 3, 0, 0, 7, 8, 1, 1, 4, 4, 4, 3, 6, 1, 3, 8, 5, 3, 4, 5, 4, 7, 7, 0, 1, 5, 0, 4, 8, 1, 7, 9, 2, 8, 1, 3, 0, 3, 3, 3, 1, 5, 0, 0, 9, 4, 4, 5, 0, 3, 3, 0, 4, 7, 6, 9, 7, 7, 4, 2, 7, 3, 2, 7, 1, 3, 9, 3, 0, 4, 3, 5, 6, 2, 4, 8, 3, 1, 4, 7, 9
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
By summing over g(1)-g(5) and g(2)-g(4) separately we obtain A214552 for the first difference and a quarter of A086724 for the second difference. - R. J. Mathar, Jul 20 2012
2/3 times this constant equals A086724 [Bailey, Borwein and Crandall, 2006] - R. J. Mathar, Jul 20 2012
|
|
REFERENCES
|
L. Fejes Tóth, Lagerungen in der Ebene, auf der Kugel und im Raum, 2nd. ed., Springer-Verlag, Berlin, Heidelberg 1972; see p. 213.
|
|
LINKS
|
|
|
FORMULA
|
Equals Integral_{x>=0} x/(exp(x) + exp(-x) - 1) dx. - Amiram Eldar, May 22 2023
|
|
EXAMPLE
|
1.1719536193447294453... = A214552 + A086724/4 = 1/1^2 +1/2^2 -1/4^2 -1/5^2 +1/7^2 +1/8^2 -1/10^2 -1/11^2 ++--....
|
|
MATHEMATICA
|
g[k_] := PolyGamma[1, k/6]/36; RealDigits[g[1] + g[2] - g[4] - g[5], 10, 99] // First (* Jean-François Alcover, Feb 12 2013 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|