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A259073 Decimal expansion of zeta'(-8) (the derivative of Riemann's zeta function at -8). 21
0, 0, 8, 3, 1, 6, 1, 6, 1, 9, 8, 5, 6, 0, 2, 2, 4, 7, 3, 5, 9, 5, 2, 4, 4, 2, 6, 5, 1, 0, 5, 3, 4, 2, 1, 4, 2, 2, 5, 6, 7, 4, 1, 2, 2, 9, 1, 8, 8, 2, 9, 9, 9, 9, 0, 4, 0, 2, 1, 0, 5, 3, 2, 7, 5, 3, 0, 5, 6, 9, 1, 7, 4, 0, 7, 8, 8, 1, 2, 3, 5, 3, 8, 3, 4, 8, 3, 4, 5, 2, 5, 1, 4, 5, 2, 4, 4, 0, 3, 5, 1, 7, 4, 1, 2, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15.1 Generalized Glaisher constants, p. 136-137.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2000

Eric Weisstein's MathWorld, Riemann Zeta Function.

Wikipedia, Riemann Zeta Function

FORMULA

zeta'(-n) = (BernoulliB(n+1)*HarmonicNumber(n))/(n+1) - log(A(n)), where A(n) is the n-th Bendersky constant, that is the n-th generalized Glaisher constant.

zeta'(-8) = 315*zeta(9)/(4*Pi^8) = -log(A(8)).

EXAMPLE

0.0083161619856022473595244265105342142256741229188299990402105327530569174...

MATHEMATICA

Join[{0, 0}, RealDigits[Zeta'[-8], 10, 104] // First]

PROG

(PARI) zeta'(-8) \\ Altug Alkan, Dec 08 2015

CROSSREFS

Cf. A075700 (zeta'(0)), A084448 (zeta'(-1)), A240966 (zeta'(-2)), A259068 (zeta'(-3)), A259069 (zeta'(-4)), A259070 (zeta'(-5)), A259071 (zeta'(-6)), A259072 (zeta'(-7)).

Sequence in context: A021550 A092555 A001061 * A075525 A242048 A097890

Adjacent sequences:  A259070 A259071 A259072 * A259074 A259075 A259076

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Jun 18 2015

STATUS

approved

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)