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 A110544 #42 May 30 2025 10:05:18
%S A110544 0,8,1,0,6,1,4,6,6,7,9,5,3,2,7,2,5,8,2,1,9,6,7,0,2,6,3,5,9,4,3,8,2,3,
%T A110544 6,0,1,3,8,6,0,2,5,2,6,3,6,2,2,1,6,5,8,7,1,8,2,8,4,8,4,5,9,5,1,7,2,3,
%U A110544 4,3,0,4,0,7,2,7,3,9,6,0,2,3,0,5,2,5,6,7,0,1,3,6,4,0,4,5,8,0,2,3,7,7,9,9,4,3
%N A110544 Decimal expansion of -Integral {x=1..2} log gamma(x) dx.
%D A110544 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.21, p. 168.
%H A110544 Rafael Jakimczuk, <a href="http://dx.doi.org/10.13140/RG.2.2.13911.18084">Two Topics in Number Theory: Products Related with the e Number and Sum of Subscripts in Prime Numbers</a>, ResearchGate, May 2025. See p. 2, the constant C in eq. (2.1).
%H A110544 Paul J. Nahin, <a href="https://doi.org/10.1007/978-3-030-43788-6">Inside interesting integrals</a>, Undergrad. Lecture Notes in Physics, Springer (2020), p. 39, eq. (1.8.1).
%H A110544 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LogGammaFunction.html">Log Gamma Function</a>.
%H A110544 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GammaFunction.html">Gamma Function</a>.
%F A110544 Equals zeta'(0)+1 = -1/2*log(2*Pi)+1. - _Jean-François Alcover_, Jun 10 2013
%F A110544 From _Amiram Eldar_, Jul 05 2020: (Start)
%F A110544 Equals Sum_{k>=2} (1/(k + 1) - 1/(2*k))*(zeta(k)-1).
%F A110544 Equals Integral_{x=0..1} (1/2 - 1/(1 - x) - 1/log(x)) dx/log(x). (End)
%F A110544 Equals -Integral_{x=1..oo} ({x}-1/2)/x dx, where {.} is the fractional part [Nahin]. - _R. J. Mathar_, May 16 2024
%F A110544 Equals 1 - A075700 = log(A229495). - _Hugo Pfoertner_, Sep 05 2024
%F A110544 Equals log(2) - (gamma+1)/2 - Sum_{k>=2} (-1)^k*(zeta(k)-1)/(k+1), where gamma is Euler's constant (A001620) (Jakimczuk, 2025). - _Amiram Eldar_, May 30 2025
%e A110544 0.081061466795327258219670263594382360138602526362216587182848459...
%t A110544 RealDigits[ N[ -Integrate[ Log[ Gamma[ x]], {x, 1, 2}], 128], 10, 128]
%t A110544 RealDigits[ 1/2*Log[2*Pi]-1, 10, 105] // First // Prepend[#, 0]& (* _Jean-François Alcover_, Jun 10 2013 *)
%o A110544 (PARI) -intnum(x=1, 2, log(gamma(x))) \\ _Michel Marcus_, Jul 05 2020
%Y A110544 Cf. A001620, A075700, A110543, A229495.
%K A110544 cons,nonn
%O A110544 0,2
%A A110544 _Robert G. Wilson v_, Jul 25 2005