A271526 Decimal expansion of the negated imaginary part of the derivative of the Dirichlet function eta(z), at z=i, the imaginary unit.

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, 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, 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

Offset

-1,1

Comments

The corresponding real part of eta'(i) is in A271525.

Links

Stanislav Sykora, Table of n, a(n) for n = -1..2000

Eric Weisstein's World of Mathematics, Dirichlet Eta Function

Formula

Equals -imag(eta'(i)).

Example

-0.06932826039035741016424390275838846419219731377645821026096551065...

Mathematica

RealDigits[Im[2^(1-I)*Log[2]*Zeta[I] + (1 - 2^(1-I))*Zeta'[I]], 10, 120][[1]] (* Vaclav Kotesovec, Apr 10 2016 *)
RealDigits[Im[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);
imag(derdireta(I)) \\ Evaluation

Crossrefs

Cf. A271523 (real(eta(i))), A271524 (imag(eta(i))), A271525(real(eta'(i))).

Sequence in context: A013707 A002162 A257945 * A072365 A239068 A259833

Adjacent sequences: A271523 A271524 A271525 * A271527 A271528 A271529

Keyword

nonn,cons

Author

Stanislav Sykora, Apr 09 2016

Status

approved