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

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, 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, 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

Offset: 0

Author

Stanislav Sykora, Apr 09 2016

Keywords

• nonn
• cons

Comments

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

Examples

			0.235920948050440923634079267603058434760419573589591512948304660...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..2000
• Eric Weisstein's World of Mathematics, Dirichlet Eta Function

Crossrefs

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

Programs

Mathematica

RealDigits[Re[2^(1-I)*Log[2]*Zeta[I] + (1 - 2^(1-I))*Zeta'[I]], 10, 120][[1]] (* Vaclav Kotesovec, Apr 10 2016 *)
RealDigits[Re[DirichletEta'[I]], 10, 110][[1]] (* Eric W. Weisstein, Jan 06 2024 *)

PARI

\\ Derivative of Dirichlet eta function (fails for z=1):
derdireta(z)=2^(1-z)*log(2)*zeta(z)+(1-2^(1-z))*zeta'(z);
real(derdireta(I)) \\ Evaluation

Formula

Equals real(eta'(i)).