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A260660
Decimal expansion of zeta'(-13) (the derivative of Riemann's zeta function at -13).
15
0, 6, 3, 7, 4, 9, 8, 7, 3, 7, 4, 4, 5, 7, 6, 8, 8, 0, 2, 8, 6, 0, 3, 8, 6, 8, 1, 4, 7, 3, 3, 3, 5, 0, 5, 5, 6, 4, 8, 8, 2, 7, 3, 5, 5, 3, 1, 2, 7, 5, 8, 4, 9, 1, 3, 8, 5, 1, 0, 0, 8, 8, 5, 8, 8, 7, 7, 3, 7, 0, 6, 4, 2, 0, 1, 5, 6, 6, 6, 8, 7, 0, 9, 4, 7, 0, 9, 2, 6, 7, 8, 1, 5, 3, 5, 8, 2, 6, 3, 1, 8, 7, 8, 2, 4, 3, 7
OFFSET
0,2
LINKS
FORMULA
zeta'(-n) = (BernoulliB(n+1)*HarmonicNumber(n))/(n+1) - log(A(n)), where A(n) is the n-th Bendersky constant, that is the n-th generalized Glaisher constant.
zeta'(-13) = (1145993/4324320) - log(A(13)).
zeta'(-13) = 1145993/4324320 - gamma/12 - log(2*Pi)/12 + 6081075*Zeta'(14) / (8*Pi^14), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Dec 05 2015
EXAMPLE
0.06374987374457688028603868147333505564882735...
MATHEMATICA
N[Zeta'[-13]]
Join[{0}, RealDigits[Zeta'[-13], 10, 1500] // First]
PROG
(PARI) zeta'(-13) \\ Altug Alkan, Nov 13 2015
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)), A266264 (zeta'(-14)), A266270 (zeta'(-15)), A266271 (zeta'(-16)), A266272 (zeta'(-17)), A266273 (zeta'(-18)), A266274 (zeta'(-19)), A266275 (zeta'(-20)).
Sequence in context: A187747 A073223 A182549 * A011191 A246730 A200239
KEYWORD
nonn,cons
AUTHOR
G. C. Greubel, Nov 13 2015
STATUS
approved