A242617 Decimal expansion of Kuijlaars-Saff constant, a constant related to Tammes' constants, Thomson's electron problem and Fekete points.

5, 5, 3, 0, 5, 1, 2, 9, 3, 3, 5, 7, 5, 9, 5, 1, 8, 6, 7, 7, 9, 9, 5, 1, 0, 3, 7, 0, 8, 7, 1, 2, 4, 7, 7, 4, 5, 5, 0, 8, 0, 2, 8, 5, 7, 6, 0, 1, 9, 6, 6, 1, 7, 7, 6, 3, 3, 0, 4, 0, 7, 0, 9, 7, 0, 5, 9, 5, 3, 8, 7, 8, 8, 4, 0, 7, 7, 1, 2, 5, 4, 1, 6, 8, 7, 0, 5, 3, 7, 3, 2, 6, 3, 1, 6, 8, 2, 9, 1, 3

Offset: 0

Author

Jean-François Alcover, May 19 2014

Keywords

• nonn
• cons

Examples

			-0.5530512933575951867799510370871247745508...
		

References

• Steven 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 World of Mathematics, Thomson Problem
• Wikipedia, Thomson problem

Crossrefs

Cf. A059750, A080865, A242088.

Programs

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

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

Formula

sqrt(3)*sqrt(sqrt(3)/(8*Pi))*zeta(1/2)*(zeta(1/2, 1/3) - zeta(1/2, 2/3)).