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%I #19 Jan 06 2024 16:33:06
%S 6,9,3,2,8,2,6,0,3,9,0,3,5,7,4,1,0,1,6,4,2,4,3,9,0,2,7,5,8,3,8,8,4,6,
%T 4,1,9,2,1,9,7,3,1,3,7,7,6,4,5,8,2,1,0,2,6,0,9,6,5,5,1,0,6,5,5,9,5,8,
%U 9,4,2,0,6,6,9,2,6,2,3,7,7,8,4,4,1,6,6,8,9,6,5,8,7,3,0,6,0,4,7,5,0,7,1,0,6
%N Decimal expansion of the negated imaginary part of the derivative of the Dirichlet function eta(z), at z=i, the imaginary unit.
%C The corresponding real part of eta'(i) is in A271525.
%H Stanislav Sykora, <a href="/A271526/b271526.txt">Table of n, a(n) for n = -1..2000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>
%F Equals -imag(eta'(i)).
%e -0.06932826039035741016424390275838846419219731377645821026096551065...
%t RealDigits[Im[2^(1-I)*Log[2]*Zeta[I] + (1 - 2^(1-I))*Zeta'[I]], 10, 120][[1]] (* _Vaclav Kotesovec_, Apr 10 2016 *)
%t RealDigits[Im[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 imag(derdireta(I)) \\ Evaluation
%Y Cf. A271523 (real(eta(i))), A271524 (imag(eta(i))), A271525(real(eta'(i))).
%K nonn,cons
%O -1,1
%A _Stanislav Sykora_, Apr 09 2016
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