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%I #17 Apr 17 2018 09:41:44
%S 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,
%T 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,
%U 1,6,0,8,7,8,9
%N Decimal expansion of the Dirichlet beta-function at 1/2.
%C Appears in lattice sums like A088537.
%H G. C. Greubel, <a href="/A195103/b195103.txt">Table of n, a(n) for n = 0..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_beta_function">Dirichlet beta function</a>
%F Equals (zeta(1/2,1/4) - zeta(1/2,3/4))/2 where zeta(.,.) is the Hurwitz zeta-function.
%e Equals 0.66769145718960917665869...
%p DirichletBeta := proc(s) (Zeta(0,s,1/4)-Zeta(0,s,3/4))/4^s ; end proc:
%p x := evalf(DirichletBeta(1/2)) ;
%t RealDigits[ DirichletBeta[1/2], 10, 75] // First (* _Jean-François Alcover_, Feb 20 2013, updated Mar 14 2018 *)
%o (PARI) zetahurwitz(1/2,1/4)/2 - zetahurwitz(1/2,3/4)/2 \\ _Charles R Greathouse IV_, Jan 31 2018
%K nonn,cons
%O 0,1
%A _R. J. Mathar_, Sep 09 2011