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Decimal expansion of the real positive solution to eta(x) = x.
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%I #23 May 24 2021 07:42:03

%S 6,2,9,3,3,4,0,9,4,0,0,9,3,7,2,7,6,7,5,5,6,4,8,0,5,0,2,5,8,9,3,2,6,1,

%T 3,7,6,4,7,2,0,7,6,4,6,8,6,6,1,8,5,3,5,5,0,6,8,8,5,8,0,2,3,1,9,7,2,6,

%U 9,2,8,5,2,9,1,5,5,7,4,6,2,1,1,0,4,2,0,0,7,9,7,5,5,6,1,9,4

%N Decimal expansion of the real positive solution to eta(x) = x.

%C Fixed point of Dirichlet eta function.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_eta_function">Dirichlet Eta Function</a>.

%e 0.6293340940...

%t RealDigits[x /. FindRoot[DirichletEta[x] - x, {x, 0}, WorkingPrecision -> 120], 10, 100] [[1]] (* _Amiram Eldar_, May 24 2021 *)

%o (PARI) solve(n=0,2,(1-2^(1-n))*zeta(n)-n) \\ _Edward Jiang_, Sep 08 2014

%Y Cf. A197070, A267315, A267316.

%K nonn,cons

%O 0,1

%A _Michal Paulovic_, Sep 08 2014