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A271533 Decimal expansion of the derivative of the Dirichlet function eta(z) at z = -1. 1
2, 6, 5, 2, 1, 4, 3, 7, 0, 9, 1, 4, 7, 0, 4, 3, 5, 1, 1, 6, 9, 3, 4, 8, 2, 7, 3, 5, 7, 5, 6, 1, 6, 4, 0, 5, 6, 0, 0, 2, 7, 5, 7, 6, 2, 8, 8, 5, 5, 2, 0, 2, 6, 6, 2, 9, 2, 6, 7, 3, 5, 8, 2, 5, 7, 4, 2, 8, 1, 2, 2, 5, 0, 0, 9, 8, 3, 3, 2, 7, 9, 7, 4, 3, 2, 8, 7, 5, 2, 5, 3, 3, 2, 0, 5, 3, 3, 7, 0, 7, 6, 7, 7, 9, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This entry completes the values of the derivatives eta'(z) at z = 0,1,i,-1,-i (see crossrefs).

LINKS

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

Eric Weisstein's World of Mathematics, Dirichlet Eta Function

FORMULA

eta'(-1) = 3*log(A) - log(2)/3 - 1/4, where A = A074962 is the Glaisher-Kinkelin constant.

EXAMPLE

0.265214370914704351169348273575616405600275762885520266292673582574...

MATHEMATICA

RealDigits[3*Log[Glaisher] - Log[2]/3 - 1/4, 10, 120][[1]] (* G. C. Greubel, Apr 09 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);

derdireta(-1) \\ Evaluation

CROSSREFS

Cf. A074962, A256358 (eta'(0)), A091812 (eta'(1)), A271525 (real(eta'(i))), A271526 (-imag(eta'(i))) .

Sequence in context: A240023 A004583 A175995 * A021381 A157890 A198821

Adjacent sequences:  A271530 A271531 A271532 * A271534 A271535 A271536

KEYWORD

nonn,cons

AUTHOR

Stanislav Sykora, Apr 09 2016

STATUS

approved

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Last modified August 23 04:06 EDT 2017. Contains 290958 sequences.