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

0,1

References

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 8.8 p. 509.

Links

Table of n, a(n) for n=0..99.

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

Cf. A059750, A080865, A242088.

Sequence in context: A128006 A157703 A332507 * A158349 A320478 A364881

Adjacent sequences: A242614 A242615 A242616 * A242618 A242619 A242620

Keyword

nonn,cons

Author

Jean-François Alcover, May 19 2014

Status

approved