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 A243263 #42 Feb 16 2025 08:33:22
%S A243263 9,7,9,5,5,5,5,2,6,9,4,2,8,4,4,6,0,5,8,2,4,2,1,8,8,3,7,2,6,3,4,9,1,8,
%T A243263 2,6,4,4,5,5,3,6,7,5,2,4,9,5,5,2,9,9,0,2,2,5,7,7,1,7,1,4,2,7,9,7,5,8,
%U A243263 8,5,6,7,2,4,8,1,5,5,9,6,1,4,9,4,4,4,4,4,3,5,3,8,3,3,2,1,9,6
%N A243263 Decimal expansion of the generalized Glaisher-Kinkelin constant A(3).
%C A243263 Also known as the third Bendersky constant.
%D A243263 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 137.
%H A243263 G. C. Greubel, <a href="/A243263/b243263.txt">Table of n, a(n) for n = 0..10000</a>
%H A243263 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 A243263 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 A243263 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 A243263 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Glaisher-KinkelinConstant.html">Glaisher-Kinkelin Constant</a>.
%F A243263 A(k) = exp(B(k+1)/(k+1)*H(k) - zeta'(-k)), where B(k) is the k-th Bernoulli number and H(k) the k-th harmonic number.
%F A243263 A(3) = exp(-11/720 - zeta'(-3)).
%F A243263 Equals exp(3*zeta'(4)/(4*Pi^4) - gamma/120) / (2*Pi)^(1/120), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Jul 24 2015
%F A243263 Equals (2*Pi*exp(gamma) * Product_{p prime} p^(1/(p^4-1)))^c, where gamma is Euler's constant (A001620), and c = Bernoulli(4)/4 = -1/120 (Van Gorder, 2012). - _Amiram Eldar_, Feb 08 2024
%e A243263 0.97955552694284460582421883726349...
%t A243263 RealDigits[Exp[-11/720 - Zeta'[-3]], 10, 98] // First
%t A243263 RealDigits[Exp[(BernoulliB[4]/4) * (EulerGamma + Log[2 * Pi] - (Zeta'[4]/Zeta[4]))], 10, 100] // First (* _G. C. Greubel_, Dec 31 2015 *)
%o A243263 (PARI) exp(-11/720 - zeta'(-3)) \\ _Stefano Spezia_, Dec 01 2024
%Y A243263 Cf. A001620, A255321, A259068.
%Y A243263 Cf. A019727, A074962, A243262, A243263, A243264, A243265, A266553, A266554, A266555, A266556, A266557, A266558, A266559, A260662, A266560, A266562, A266563, A266564, A266565, A266566, A266567.
%K A243263 nonn,cons
%O A243263 0,1
%A A243263 _Jean-François Alcover_, Jun 02 2014