A195103 Decimal expansion of the Dirichlet beta-function at 1/2.

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

Offset: 0

Author

R. J. Mathar, Sep 09 2011

Keywords

• nonn
• cons

Comments

Appears in lattice sums like A088537.

Examples

			Equals 0.66769145718960917665869...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Wikipedia, Dirichlet beta function

Programs

Maple

DirichletBeta := proc(s) (Zeta(0,s,1/4)-Zeta(0,s,3/4))/4^s ; end proc:
x := evalf(DirichletBeta(1/2)) ;

Mathematica

RealDigits[ DirichletBeta[1/2], 10, 75] // First (* Jean-François Alcover, Feb 20 2013, updated Mar 14 2018 *)

PARI

zetahurwitz(1/2,1/4)/2 - zetahurwitz(1/2,3/4)/2 \\ Charles R Greathouse IV, Jan 31 2018

Formula

Equals (zeta(1/2,1/4) - zeta(1/2,3/4))/2 where zeta(.,.) is the Hurwitz zeta-function.