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%I #15 Aug 24 2018 17:30:53
%S 6,1,7,8,5,5,0,8,8,8,4,8,8,5,2,0,6,6,0,7,2,5,3,8,9,9,4,7,2,7,9,9,3,1,
%T 6,5,7,1,0,6,2,3,5,4,7,8,9,9,3,8,6,5,0,0,2,2,5,5,1,5,2,8,2,2,9,5,6,0,
%U 7,7,8,0,5,2,7,2,5,0,4,4,6,5,4,1,0,1,3,9,3,4,6,1,5,5,3,9,9,5,7,0,3,7,5,6,1
%N Decimal expansion of the Dirichlet beta function at 1/3.
%H G. C. Greubel, <a href="/A261622/b261622.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/DirichletBetaFunction.html">Dirichlet Beta Function</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_beta_function">Dirichlet beta function</a>
%F beta(1/3) = (zeta(1/3, 1/4) - zeta(1/3, 3/4))/2^(2/3).
%e 0.6178550888488520660725389947279931657106235478993865002255152822956...
%p evalf(Sum((-1)^n/(2*n+1)^(1/3), n=0..infinity), 120); # _Vaclav Kotesovec_, Aug 27 2015
%t RealDigits[DirichletBeta[1/3],10,105]//First
%Y Cf. A003881 (beta(1)=Pi/4), A006752 (beta(2)=Catalan), A153071 (beta(3)), A175572 (beta(4)), A175571 (beta(5)), A175570 (beta(6)), A261623 (beta(1/4)), A261624 (beta(1/5)).
%K cons,easy,nonn
%O 0,1
%A _Jean-François Alcover_, Aug 27 2015
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