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

Author

G. C. Greubel, Dec 31 2015

Keywords

• nonn
• cons

Comments

Also known as the 12th Bendersky constant.

Examples

			0.9386894455960125851529657813206767183332587685218350098663907...
		

Links

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

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.

Programs

Mathematica

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

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