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A259071
Decimal expansion of zeta'(-6) (the derivative of Riemann's zeta function at -6) (negated).
16
0, 0, 5, 8, 9, 9, 7, 5, 9, 1, 4, 3, 5, 1, 5, 9, 3, 7, 4, 5, 0, 6, 2, 9, 8, 7, 7, 4, 0, 8, 3, 9, 2, 0, 2, 5, 5, 7, 9, 8, 0, 1, 5, 3, 4, 6, 2, 0, 1, 5, 7, 1, 9, 5, 8, 6, 5, 2, 3, 9, 3, 9, 2, 2, 0, 6, 3, 5, 9, 7, 0, 3, 7, 5, 9, 4, 2, 4, 9, 0, 5, 7, 2, 3, 0, 2, 3, 8, 6, 3, 0, 0, 7, 5, 4, 2, 2, 5, 8, 3, 8, 5, 3, 6, 4, 8
OFFSET
0,3
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15.1 Generalized Glaisher constants, p. 136-137.
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'(-6) = -45*zeta(7)/(8*Pi^6) = -log(A(6)).
EXAMPLE
-0.0058997591435159374506298774083920255798015346201571958652393922063597...
MATHEMATICA
Join[{0, 0}, RealDigits[Zeta'[-6], 10, 104] // First]
PROG
(PARI) zeta'(-6) \\ Altug Alkan, Dec 11 2015
CROSSREFS
Sequence in context: A257833 A021633 A178309 * A205862 A293795 A165991
KEYWORD
nonn,cons
AUTHOR
STATUS
approved