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 A375369 #12 Aug 19 2024 03:12:53
%S A375369 0,8,8,0,0,6,8,2,4,4,2,6,1,6,6,5,8,8,8,2,6,4,4,1,7,8,2,3,6,3,5,8,0,0,
%T A375369 1,3,8,3,6,7,6,3,2,6,1,0,8,9,0,3,3,2,9,0,1,9,2,1,6,6,7,6,3,6,6,2,6,0,
%U A375369 0,0,1,6,9,2,0,7,7,9,8,5,8,4,8,3,1,8,3
%N A375369 Decimal expansion of zeta'(2)/(2*Pi^2) + zeta(3)/(4*Pi^2) + log(2*Pi)/12 -gamma/12.
%C A375369 zeta'(2)= -0.9375.. is the first derivative of the zeta function, see A073002. gamma is A001620.
%H A375369 Olivier Espinosa and Victor H. Moll, <a href="https://dx.doi.org/10.1023/A:1015706300169">On some integrals involving the Hurwitz zeta function: Part 1</a>, Raman. J. 6 (2002) 159-188, Example 6.4.
%F A375369 Equals Integral_{x=0..1} x^2* log(Gamma(x)) dx.
%e A375369 0.08800682442616658882644178236358001383676326108903...
%p A375369 Zeta(1,2)/2/Pi^2+Zeta(3)/4/Pi^2+log(2*Pi)/12-gamma/12 ; evalf(%) ;
%t A375369 RealDigits[Zeta'[2] / (2*Pi^2) + Zeta[3] / (4*Pi^2) + Log[2*Pi] / 12 - EulerGamma / 12, 10, 120, -1][[1]] (* _Amiram Eldar_, Aug 19 2024 *)
%Y A375369 Cf. A001620, A073002, A375368.
%K A375369 nonn,cons
%O A375369 0,2
%A A375369 _R. J. Mathar_, Aug 13 2024