cp's OEIS Frontend

A271525 Decimal expansion of the real part of the derivative of the Dirichlet function eta(z), at z=i, the imaginary unit.

%I A271525 #21 Feb 16 2025 08:33:33
%S A271525 2,3,5,9,2,0,9,4,8,0,5,0,4,4,0,9,2,3,6,3,4,0,7,9,2,6,7,6,0,3,0,5,8,4,
%T A271525 3,4,7,6,0,4,1,9,5,7,3,5,8,9,5,9,1,5,1,2,9,4,8,3,0,4,6,6,0,0,4,5,9,5,
%U A271525 9,5,9,8,4,0,8,0,3,1,6,2,6,5,2,4,3,4,5,7,3,8,7,0,1,0,6,7,3,6,2,1,6,0,3,7,5
%N A271525 Decimal expansion of the real part of the derivative of the Dirichlet function eta(z), at z=i, the imaginary unit.
%C A271525 The corresponding imaginary part of eta'(i) is in A271526.
%H A271525 Stanislav Sykora, <a href="/A271525/b271525.txt">Table of n, a(n) for n = 0..2000</a>
%H A271525 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>
%F A271525 Equals real(eta'(i)).
%e A271525 0.235920948050440923634079267603058434760419573589591512948304660...
%t A271525 RealDigits[Re[2^(1-I)*Log[2]*Zeta[I] + (1 - 2^(1-I))*Zeta'[I]], 10, 120][[1]] (* _Vaclav Kotesovec_, Apr 10 2016 *)
%t A271525 RealDigits[Re[DirichletEta'[I]], 10, 110][[1]] (* _Eric W. Weisstein_, Jan 06 2024 *)
%o A271525 (PARI) \\ Derivative of Dirichlet eta function (fails for z=1):
%o A271525 derdireta(z)=2^(1-z)*log(2)*zeta(z)+(1-2^(1-z))*zeta'(z);
%o A271525 real(derdireta(I)) \\ Evaluation
%Y A271525 Cf. A271523 (real(eta(i))), A271524 (imag(eta(i))), A271526(-imag(eta'(i))).
%K A271525 nonn,cons
%O A271525 0,1
%A A271525 _Stanislav Sykora_, Apr 09 2016