A257549 Decimal expansion of zeta''(0) (negated).

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

Offset

1,1

Comments

Essentially the same as A245273. - R. J. Mathar, Apr 30 2015

Links

Table of n, a(n) for n=1..104.

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

Cf. A075700, A082633, A261508, A201994.

Sequence in context: A221524 A193009 A045866 * A112964 A368845 A350791

Adjacent sequences: A257546 A257547 A257548 * A257550 A257551 A257552

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 29 2015

Status

approved