A266260 Decimal expansion of zeta'(-9) (the derivative of Riemann's zeta function at -9).

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

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1501

Formula

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

zeta'(-9) = 7129/332640 - log(A(9)).

Example

0.0031301453197885727549257682907854467026693658654815.....

Mathematica

Join[{0, 0}, RealDigits[Zeta'[-9], 10, 100] // First]
N[Zeta'[-9], 100]

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)), 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)), A266274 (zeta'(-19)), A266275 (zeta'(-20)).

Sequence in context: A201679 A131088 A136157 * A143353 A127172 A011087

Adjacent sequences: A266257 A266258 A266259 * A266261 A266262 A266263

Keyword

nonn,cons,easy

Author

G. C. Greubel, Dec 25 2015

Status

approved