OFFSET
0,1
REFERENCES
S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 8.8 p. 509.
LINKS
A. B. J. Kuijlaars and E. B. Saff, Asymptotics for minimal discrete energy on the sphere
Eric Weisstein's MathWorld, Thomson Problem
Wikipedia, Thomson problem
FORMULA
sqrt(3)*sqrt(sqrt(3)/(8*Pi))*zeta(1/2)*(zeta(1/2, 1/3) - zeta(1/2, 2/3)).
EXAMPLE
-0.5530512933575951867799510370871247745508...
MATHEMATICA
c = Sqrt[3]*Sqrt[Sqrt[3]/(8*Pi)]*Zeta[1/2]*(Zeta[1/2, 1/3] - Zeta[1/2, 2/3]); RealDigits[c, 10, 100] // First
PROG
(PARI) sqrt(sqrt(27)/8/Pi)*zeta(1/2)*(zetahurwitz(1/2, 1/3) - zetahurwitz(1/2, 2/3)) \\ Charles R Greathouse IV, Jan 31 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, May 19 2014
STATUS
approved