cp's OEIS Frontend

A271524 Decimal expansion of the imaginary part of the Dirichlet function eta(z), at z=i, the imaginary unit.

%I A271524 #21 Feb 16 2025 08:33:33
%S A271524 2,2,9,3,8,4,8,5,7,7,2,8,5,2,5,8,9,2,4,5,7,8,8,6,7,3,3,5,5,8,0,8,1,9,
%T A271524 3,8,2,2,5,1,9,5,4,1,5,2,6,6,1,2,1,0,3,4,6,2,5,0,7,2,3,9,3,6,7,2,9,1,
%U A271524 8,3,5,1,4,8,9,5,9,7,5,6,2,6,4,4,6,3,6,4,4,4,7,3,7,4,1,7,6,5,5,4,8,4,2,9,5
%N A271524 Decimal expansion of the imaginary part of the Dirichlet function eta(z), at z=i, the imaginary unit.
%C A271524 The corresponding real part of eta(i) is in A271523.
%H A271524 Stanislav Sykora, <a href="/A271524/b271524.txt">Table of n, a(n) for n = 0..2000</a>
%H A271524 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>
%F A271524 Equals imag(eta(i)).
%e A271524 0.229384857728525892457886733558081938225195415266121034625072393...
%t A271524 First[RealDigits[Im[(1 - 2^(1 - I))*Zeta[I]], 10, 110]] (* _Robert Price_, Apr 09 2016 *)
%o A271524 (PARI) \\ The Dirichlet eta function (fails for z=1):
%o A271524 direta(z)=(1-2^(1-z))*zeta(z);
%o A271524 imag(direta(I))\\ Evaluation
%Y A271524 Cf. A002162 (eta(1)), A179311 (real(zeta(i))), A179836 (imag(-zeta(i))), A271523 (real(eta(i))), A271525 (real(eta'(i))), A271526(-imag(eta'(i))).
%K A271524 nonn,cons
%O A271524 0,1
%A A271524 _Stanislav Sykora_, Apr 09 2016