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A295874 Decimal expansion of the real positive fixed point of the Dirichlet beta function.

%I A295874 #24 Feb 16 2025 08:33:52
%S A295874 7,2,6,5,6,4,1,9,3,2,7,4,0,4,3,6,2,6,4,4,1,6,2,4,1,3,0,1,0,1,1,3,3,4,
%T A295874 1,5,5,0,4,3,3,0,8,4,7,2,3,9,1,2,0,0,2,2,4,2,0,2,8,4,1,0,3,4,6,4,5,4,
%U A295874 3,1,7,4,8,1,3,3,2,2,0,8,1,3,2,2,2,0,2,4,6,5,7,6,3,4,1,0,2,0,7,9,6,3,4,0,5,5,6
%N A295874 Decimal expansion of the real positive fixed point of the Dirichlet beta function.
%H A295874 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/DirichletBetaFunction.html">Dirichlet Beta Function</a>.
%H A295874 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_beta_function">Dirichlet beta function</a>.
%e A295874 0.72656419327404362644162413010113341550433084723912002242028410346454317481...
%p A295874 Digits:= 140:
%p A295874 f:= s-> sum((-1)^n/(2*n+1)^s, n=0..infinity):
%p A295874 fsolve(f(x)=x, x);  # _Alois P. Heinz_, Feb 05 2018
%t A295874 RealDigits[ FindRoot[ DirichletBeta[x] == x, {x, 0}, WorkingPrecision -> 2^7, AccuracyGoal -> 2^8, PrecisionGoal -> 2^7][[1, 2]], 10, 111][[1]] (* _Robert G. Wilson v_, Jan 07 2018 *)
%o A295874 (PARI) solve(x=0,1,sumalt(n=0,((-1)^n)/(2*n+1)^x)-x)
%Y A295874 Cf. A261624.
%K A295874 nonn,cons
%O A295874 0,1
%A A295874 _Michal Paulovic_, Dec 31 2017