A259072 Decimal expansion of zeta'(-7) (the derivative of Riemann's zeta function at -7) (negated).

0, 0, 0, 7, 2, 8, 6, 4, 2, 6, 8, 0, 1, 5, 9, 2, 4, 0, 6, 5, 2, 4, 6, 7, 2, 3, 3, 3, 5, 4, 6, 5, 0, 3, 6, 0, 6, 1, 1, 9, 0, 2, 8, 8, 7, 7, 2, 0, 9, 2, 5, 4, 1, 8, 3, 1, 8, 6, 3, 6, 3, 8, 6, 1, 5, 4, 1, 4, 2, 5, 9, 7, 5, 4, 5, 5, 2, 7, 3, 0, 9, 9, 1, 3, 0, 2, 3, 2, 4, 6, 4, 4, 1, 6, 8, 0, 4, 4, 9, 3, 7, 9, 6, 0, 6, 5, 4

Offset: 0

Author

Jean-François Alcover, Jun 18 2015

Keywords

• nonn
• cons

Examples

			-0.000728642680159240652467233354650360611902887720925418318636386154...
		

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..10000
• Eric Weisstein's MathWorld, Riemann Zeta Function.
• Wikipedia, Riemann Zeta Function
• Index entries for constants related to zeta

Programs

Mathematica

Join[{0, 0, 0}, RealDigits[Zeta'[-7], 10, 104] // First]

PARI

-zeta'(-7) \\ Charles R Greathouse IV, Dec 04 2016

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'(-7) = -121/11200 - log(A(7)).

Equals -121/11200 + (gamma + log(2*Pi))/240 - 315*Zeta'(8)/(8*Pi^8), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jul 25 2015