A266559 Decimal expansion of the generalized Glaisher-Kinkelin constant A(12).

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

Offset

0,1

Comments

Also known as the 12th Bendersky constant.

Links

G. C. Greubel, Table of n, a(n) for n = 0..2000

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(12) = exp(-zeta'(-12)) = exp((B(12)/4)*(zeta(13)/zeta(12))).

A(12) = exp(-12! * Zeta(13) / (2^13 * Pi^12)). - Vaclav Kotesovec, Jan 01 2016

Example

0.9386894455960125851529657813206767183332587685218350098663907...

Mathematica

RealDigits[Exp[N[(BernoulliB[12]/4)*(Zeta[13]/Zeta[12]), 200]]][[1]] (* Program amended by Harvey P. Dale, Aug 16 2021 *)

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)), A266555 (A(8)), A266556 (A(9)), A266557 (A(10)), A266558 (A(11)), 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. A013670, A013671, A266263, A027641, A027642.

Sequence in context: A010539 A284832 A358942 * A111971 A181045 A242815

Adjacent sequences: A266556 A266557 A266558 * A266560 A266561 A266562

Keyword

nonn,cons

Author

G. C. Greubel, Dec 31 2015

Status

approved