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A271523 Decimal expansion of the real part of the Dirichlet function eta(z), at z=i, the imaginary unit.

%I A271523 #22 Feb 16 2025 08:33:33
%S A271523 5,3,2,5,9,3,1,8,1,7,6,3,0,9,6,1,6,6,5,7,0,9,6,5,0,0,8,1,9,7,3,1,9,0,
%T A271523 4,4,7,2,7,7,8,5,7,6,8,1,4,3,4,9,2,1,9,2,2,3,9,7,4,8,7,2,5,9,5,9,4,3,
%U A271523 8,2,6,3,1,5,6,3,1,1,1,7,7,6,6,8,6,6,0,8,9,6,4,8,9,7,7,9,5,5,7,2,2,4,1,2,0
%N A271523 Decimal expansion of the real part of the Dirichlet function eta(z), at z=i, the imaginary unit.
%C A271523 The corresponding imaginary part of eta(i) is in A271524.
%H A271523 Stanislav Sykora, <a href="/A271523/b271523.txt">Table of n, a(n) for n = 0..2000</a>
%H A271523 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>
%F A271523 Equals real(eta(i)).
%e A271523 0.53259318176309616657096500819731904472778576814349219223974872595...
%t A271523 First[RealDigits[Re[(1 - 2^(1 - I))*Zeta[I]], 10, 110]] (* _Robert Price_, Apr 09 2016 *)
%o A271523 (PARI) \\ The Dirichlet eta function (fails for z=1):
%o A271523 direta(z)=(1-2^(1-z))*zeta(z);
%o A271523 real(direta(I)) \\ Evaluation
%Y A271523 Cf. A002162 (eta(1)), A179311 (real(zeta(i))), A179836 (imag(-zeta(i))), A271524 (imag(eta(i))), A271525 (real(eta'(i))), A271526(-imag(eta'(i))).
%K A271523 nonn,cons
%O A271523 0,1
%A A271523 _Stanislav Sykora_, Apr 09 2016