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A258815 Decimal expansion of the Dirichlet beta function of 8.

%I A258815 #28 Feb 16 2025 08:33:25
%S A258815 9,9,9,8,4,9,9,9,0,2,4,6,8,2,9,6,5,6,3,3,8,0,6,7,0,5,9,2,4,0,4,6,3,7,
%T A258815 8,1,4,7,6,0,0,7,4,3,3,0,0,7,4,2,8,0,6,9,7,2,4,9,8,7,4,2,9,2,4,0,6,7,
%U A258815 1,1,5,9,3,2,5,0,7,1,7,3,5,1,1,2,6,4,2,7,0,5,0,8,1,3,5,7,0,4,2,6,2,1,2,8,3
%N A258815 Decimal expansion of the Dirichlet beta function of 8.
%H A258815 G. C. Greubel, <a href="/A258815/b258815.txt">Table of n, a(n) for n = 0..10000</a>
%H A258815 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletBetaFunction.html">Dirichlet Beta Function</a>.
%H A258815 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_beta_function">Dirichlet beta function</a>.
%F A258815 beta(8) = Sum_{n>=0} (-1)^n/(2n+1)^8 = (zeta(8, 1/4) - zeta(8, 3/4))/65536 = (PolyGamma(7, 1/4) - PolyGamma(7, 3/4))/330301440.
%F A258815 Equals ClausenFunction(8, Pi/2).
%F A258815 Equals Product_{p prime >= 3} (1 - (-1)^((p-1)/2)/p^8)^(-1). - _Amiram Eldar_, Nov 06 2023
%e A258815 0.99984999024682965633806705924046378147600743300742806972498742924...
%t A258815 RealDigits[DirichletBeta[8], 10, 102] // First
%o A258815 (PARI) (zetahurwitz(8,1/4)-zetahurwitz(8,3/4))*(1/4)^8 \\ _Hugo Pfoertner_, Feb 07 2020
%Y A258815 Cf. A003881 (beta(1)=Pi/4), A006752 (beta(2)=Catalan), A153071 (beta(3)), A175572 (beta(4)), A175571 (beta(5)), A175570 (beta(6)), A258814 (beta(7)), A258816 (beta(9)).
%K A258815 nonn,cons,easy
%O A258815 0,1
%A A258815 _Jean-François Alcover_, Jun 11 2015