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A271526 Decimal expansion of the negated imaginary part of the derivative of the Dirichlet function eta(z), at z=i, the imaginary unit. 5
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 (list; constant; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified May 23 04:09 EDT 2017. Contains 286909 sequences.