OFFSET
1,1
COMMENTS
Essentially the same as A245273. - R. J. Mathar, Apr 30 2015
LINKS
Tom M. Apostol, Formulas for higher derivatives of the Riemann zeta function, Mathematics of Computation 44 (1985), p. 223-232.
Richard E. Crandall, Unified algorithms for polylogarithm, L-series, and zeta variants. p. 15.
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 104.
Eric Weisstein's World of Mathematics, Riemann Zeta Function.
Eric Weisstein's World of Mathematics, Stieltjes Constants.
FORMULA
zeta''(0) = gamma_1 + gamma^2/2 - Pi^2/24 - (1/2)*(log(2)+log(Pi))^2, where gamma_1 is the first Stieltjes constant.
EXAMPLE
2.00635645590858485121010002672996043819899491016091988116986828...
MAPLE
evalf(-Zeta(2, 0), 120); # Vaclav Kotesovec, Apr 29 2015
MATHEMATICA
RealDigits[ StieltjesGamma[1] + EulerGamma^2/2 - Pi^2/24 - (1/2)*(Log[2] + Log[Pi])^2, 10, 104] // First
PROG
(PARI) -zeta''(0) \\ Charles R Greathouse IV, Mar 10 2016
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Apr 29 2015
STATUS
approved