This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A266558 #23 Feb 16 2025 08:33:28
%S A266558 9,5,0,3,3,1,2,4,8,4,5,3,2,8,8,8,6,6,5,1,4,2,3,3,8,4,1,0,1,5,3,3,1,2,
%T A266558 7,1,5,9,7,5,6,6,4,0,3,4,5,6,1,7,3,0,4,0,8,6,1,0,8,8,8,8,1,1,6,2,2,9,
%U A266558 7,8,4,9,1,7,7,3,4,4,4,5,1
%N A266558 Decimal expansion of the generalized Glaisher-Kinkelin constant A(11).
%C A266558 Also known as the 11th Bendersky constant.
%H A266558 G. C. Greubel, <a href="/A266558/b266558.txt">Table of n, a(n) for n = 0..2000</a>
%H A266558 Victor S. Adamchik, <a href="https://doi.org/10.1016/S0377-0427(98)00192-7">Polygamma functions of negative order</a>, Journal of Computational and Applied Mathematics, Vol. 100, No. 2 (1998), pp. 191-199.
%H A266558 L. Bendersky, <a href="https://doi.org/10.1007/BF02547794">Sur la fonction gamma généralisée</a>, Acta Mathematica , Vol. 61 (1933), pp. 263-322; <a href="https://projecteuclid.org/journals/acta-mathematica/volume-61/issue-none/Sur-la-fonction-gamma-g%C3%A9n%C3%A9ralis%C3%A9e/10.1007/BF02547794.full">alternative link</a>.
%H A266558 Robert A. Van Gorder, <a href="https://doi.org/10.1142/S1793042112500297">Glaisher-type products over the primes</a>, International Journal of Number Theory, Vol. 8, No. 2 (2012), pp. 543-550.
%H A266558 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Glaisher-KinkelinConstant.html">Glaisher-Kinkelin Constant</a>.
%F A266558 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.
%F A266558 A(11) = exp(H(11)*B(12)/12 - zeta'(-11)) = exp((B(12)/12)*(EulerGamma + log(2*Pi) - (zeta'(12)/zeta(12)))).
%F A266558 Equals (2*Pi*exp(gamma) * Product_{p prime} p^(1/(p^12-1)))^c, where gamma is Euler's constant (A001620), and c = Bernoulli(12)/12 = -691/32760 (Van Gorder, 2012). - _Amiram Eldar_, Feb 08 2024
%e A266558 0.950331248453288866514233841015331271597566403456173040861088881...
%t A266558 Exp[N[(BernoulliB[12]/12)*(EulerGamma + Log[2*Pi] - Zeta'[12]/Zeta[12]), 200]]
%Y A266558 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)), 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)).
%Y A266558 Cf. A001620, A013670, A266262, A027641, A027642, A001008, A002805.
%K A266558 nonn,cons
%O A266558 0,1
%A A266558 _G. C. Greubel_, Dec 31 2015