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

0,1

Comments

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

Links

Stanislav Sykora, Table of n, a(n) for n = 0..2000

Eric Weisstein's World of Mathematics, Dirichlet Eta Function

Formula

Equals real(eta'(i)).

Example

0.235920948050440923634079267603058434760419573589591512948304660...

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A279074 A120495 A107477 * A357101 A232562 A064358

Adjacent sequences: A271522 A271523 A271524 * A271526 A271527 A271528

Keyword

nonn,cons

Author

Stanislav Sykora, Apr 09 2016

Status

approved