A271525 - OEIS

%I #20 Jan 06 2024 16:33:23

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

%C The corresponding imaginary part of eta'(i) is in A271526.

%H Stanislav Sykora, <a href="/A271525/b271525.txt">Table of n, a(n) for n = 0..2000</a>

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

%F Equals real(eta'(i)).

%e 0.235920948050440923634079267603058434760419573589591512948304660...

%t RealDigits[Re[2^(1-I)*Log[2]*Zeta[I] + (1 - 2^(1-I))*Zeta'[I]], 10, 120][[1]] (* _Vaclav Kotesovec_, Apr 10 2016 *)

%t RealDigits[Re[DirichletEta'[I]], 10, 110][[1]] (* _Eric W. Weisstein_, Jan 06 2024 *)

%o (PARI) \\ Derivative of Dirichlet eta function (fails for z=1):

%o derdireta(z)=2^(1-z)*log(2)*zeta(z)+(1-2^(1-z))*zeta'(z);

%o real(derdireta(I)) \\ Evaluation

%Y Cf. A271523 (real(eta(i))), A271524 (imag(eta(i))), A271526(-imag(eta'(i))).

%K nonn,cons

%O 0,1

%A _Stanislav Sykora_, Apr 09 2016