A266274 Decimal expansion of zeta'(-19) (the derivative of Riemann's zeta function at -19) (negated).
2, 9, 9, 6, 5, 5, 2, 9, 8, 3, 1, 3, 9, 2, 3, 5, 1, 9, 3, 9, 4, 3, 1, 8, 6, 5, 2, 9, 7, 2, 7, 4, 2, 0, 1, 7, 9, 1, 9, 0, 8, 2, 2, 6, 1, 0, 9, 1, 1, 5, 5, 6, 5, 9, 1, 5, 8, 8, 1, 8, 7, 1, 6, 6, 8, 2, 0, 5, 7, 6, 1, 6, 0, 2, 8, 6, 7, 6, 7, 7, 6, 1, 1, 7, 2, 6, 8, 7, 3, 6, 3, 0, 3, 4
Offset: 2
Examples
-29.965529831392351939431865297274201791908226109115565915881....
Links
- G. C. Greubel, Table of n, a(n) for n = 2..1500
Crossrefs
Cf. A075700 (zeta'(0)), A084448 (zeta'(-1)), A240966 (zeta'(-2)), A259068 (zeta'(-3)), A259069 (zeta'(-4)), A259070 (zeta'(-5)), A259071 (zeta'(-6)), A259072 (zeta'(-7)), A259073 (zeta'(-8)), A266260 (zeta'(-9)), A266261 (zeta'(-10)), A266262 (zeta'(-11)), A266263 (zeta'(-12)), A260660 (zeta'(-13)), A266264 (zeta'(-14)), A266270 (zeta'(-15)), A266271 (zeta'(-16)), A266272 (zeta'(-17)), A266273 (zeta'(-18)), A266275 (zeta'(-20)).
Programs
-
Mathematica
RealDigits[N[Zeta'[-19], 100]]
Formula
zeta'(-n) = (BernoulliB(n+1)*HarmonicNumber(n))/(n+1) - log(A(n)), where A(n) is the n-th Bendersky constant.
zeta'(-19) = -48069674759189/512143632000 - log(A(19)).
Extensions
Offset corrected by Rick L. Shepherd, May 30 2016