A266555 Decimal expansion of the generalized Glaisher-Kinkelin constant A(8).

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

G. C. Greubel, Table of n, a(n) for n = 0..2001

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)).

Cf. A013666, A013667, A259073, A027641, A027642.

Sequence in context: A019788 A175618 A346439 * A343367 A145280 A144667

Adjacent sequences: A266552 A266553 A266554 * A266556 A266557 A266558

Keyword

nonn,cons

Author

G. C. Greubel, Dec 31 2015

Status

approved