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A266555
Decimal expansion of the generalized Glaisher-Kinkelin constant A(8).
19
9, 9, 1, 7, 1, 8, 3, 2, 1, 6, 3, 2, 8, 2, 2, 1, 9, 6, 9, 9, 9, 5, 4, 7, 4, 8, 2, 7, 6, 5, 7, 9, 3, 3, 3, 9, 8, 6, 7, 8, 5, 9, 7, 6, 0, 5, 7, 3, 0, 5, 0, 7, 9, 2, 4, 7, 0, 7, 6, 5, 9, 9, 3, 4, 0, 9, 5, 0, 2, 3, 7, 9, 3, 4, 2, 1, 7, 6, 1, 9, 0, 9, 3, 0, 9, 1, 2, 3, 8, 8, 8, 6, 1
OFFSET
0,1
COMMENTS
Also known as the 8th Bendersky constant.
LINKS
FORMULA
A(k) = exp(H(k)*B(k+1)/(k+1) - zeta'(-k)), where B(k) is the k-th Bernoulli number, H(k) the k-th harmonic number, and zeta'(x) is the derivative of the Riemann zeta function.
A(8) = -zeta'(-8) = (B(8)/4)*(zeta(9)/zeta(8)).
A(8) = exp(-8! * Zeta(9) / (2^9 * Pi^8)). - Vaclav Kotesovec, Jan 01 2016
EXAMPLE
0.99171832163282219699954748276579333986785976057305079247...
MATHEMATICA
Exp[N[(BernoulliB[8]/4)*(Zeta[9]/Zeta[8]), 200]]
CROSSREFS
Cf. A019727 (A(0)), A074962 (A(1)), A243262 (A(2)), A243263 (A(3)), A243264 (A(4)), A243265 (A(5)), A266553 (A(6)), A266554 (A(7)), A266556 (A(9)), A266557 (A(10)), A266558 (A(11)), A266559 (A(12)), A260662 (A(13)), A266560 (A(14)), A266562 (A(15)), A266563 (A(16)), A266564 (A(17)), A266565 (A(18)), A266566 (A(19)), A266567 (A(20)).
Sequence in context: A019788 A175618 A346439 * A343367 A145280 A144667
KEYWORD
nonn,cons
AUTHOR
G. C. Greubel, Dec 31 2015
STATUS
approved