A266272 Decimal expansion of zeta'(-17) (the derivative of Riemann's zeta function at -17).

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

Offset: 1

Author

G. C. Greubel, Dec 25 2015

Keywords

• nonn
• cons

Examples

			3.1286453321241578756844526391533305482263390775654797424916577061....
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..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)), A266273 (zeta'(-18)), A266274 (zeta'(-19)), A266275 (zeta'(-20)).

Programs

Mathematica

RealDigits[N[Zeta'[-17], 100]]

Formula

zeta'(-n) = HarmonicNumber(n)*BernoulliB(n+1)/(n+1) - log(A(n)), where A(n) is the n-th Bendersky constant.

zeta'(-17) = 1848652896341/175991175360 - log(A(17)).

Extensions

Offset corrected by Rick L. Shepherd, May 21 2016