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%I #14 Nov 07 2023 04:56:50
%S 9,9,9,9,4,9,6,8,4,1,8,7,2,2,0,0,8,9,8,2,1,3,5,8,8,7,3,2,9,3,8,4,7,5,
%T 2,7,3,7,2,7,4,7,9,9,6,9,1,7,9,6,1,6,0,1,2,2,3,1,6,2,7,2,3,0,8,2,9,7,
%U 8,6,5,1,3,7,9,0,4,8,5,6,3,8,8,6,1,7,1,3,9,0,2,5,8,3,2,6,5,2,9,7,3,0,7,8
%N Decimal expansion of the Dirichlet beta function of 9.
%H G. C. Greubel, <a href="/A258816/b258816.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <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(9) = Sum_{n>=0} (-1)^n/(2n+1)^9 = (zeta(9, 1/4) - zeta(9, 3/4))/262144 = 277*Pi^9/8257536.
%F Equals Product_{p prime >= 3} (1 - (-1)^((p-1)/2)/p^9)^(-1). - _Amiram Eldar_, Nov 06 2023
%e 0.999949684187220089821358873293847527372747996917961601223162723...
%t RealDigits[DirichletBeta[9], 10, 104] // First
%o (PARI) default(realprecision, 100); 277*Pi^9/8257536 \\ _G. C. Greubel_, Aug 24 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); 277*Pi(R)^9/8257536; // _G. C. Greubel_, Aug 24 2018
%Y 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)), A258815 (beta(8)).
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Jun 11 2015
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