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
David H. Bailey, Jonathan M. Borwein, and Richard E. Crandall, Integrals of the Ising class, Journal of Physics A: Mathematical and General, Vol. 39, No. 40 (2006), 12271; alternative link.
FORMULA
Equals -Integral_{x=0..1} log(x)/(x^2-x+1) dx. - Jean-François Alcover, Aug 29 2014
Equals Integral_{x>=0} x/(exp(x) + exp(-x) - 1) dx. - Amiram Eldar, May 22 2023
EXAMPLE
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
nonn,cons
AUTHOR
N. J. A. Sloane, Jul 31 2003
STATUS
approved