A259073 Decimal expansion of zeta'(-8) (the derivative of Riemann's zeta function at -8).

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

Offset: 0

Author

Jean-François Alcover, Jun 18 2015

Keywords

• nonn
• cons

Examples

			0.0083161619856022473595244265105342142256741229188299990402105327530569174...
		

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
• Index entries for constants related to zeta

Programs

Mathematica

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

PARI

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

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)).