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 A386718 #10 Jul 31 2025 06:58:07
%S A386718 5,0,0,4,4,5,3,6,2,1,7,8,5,8,0,0,2,3,4,9,6,3,3,9,4,7,8,8,1,0,1,0,5,1,
%T A386718 5,2,7,7,5,1,0,9,9,0,5,4,4,5,0,8,4,7,2,8,7,3,3,5,9,0,0,0,7,5,8,2,4,5,
%U A386718 9,0,8,4,4,8,4,9,8,7,0,2,1,0,2,7,1,2,8,9,6,3,6,4,3,7,8,4,5,3,3,7,4,9,0,8,8
%N A386718 Decimal expansion of Integral_{x=0..1} Integral_{y=0..1} Integral_{z=0..1} {1/(x*y*z)} dx dy dz, where {} denotes fractional part.
%D A386718 Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, New York: Springer, 2013. See section 2.43, page 106.
%H A386718 Yaming Yu, <a href="https://web.archive.org/web/20150910082356/https://www.siam.org/journals/problems/downloadfiles/07-002s.pdf">A Multiple Integral in Terms of Stieltjes Constants</a>, SIAM Problems and Solutions, Classical Analysis, Integrals, Problem 07-002 (2007).
%F A386718 Equals 1 - gamma - gamma_1 - gamma_2/2, where gamma_k is the k-th Stieltjes constant.
%F A386718 In general, for m >= 1, Integral_{x_1=0..1} ... Integral_{x_m=0..1} {1/(x_1*...*x_m)} dx_1 ... dx_m = 1 - Sum_{k=0..m-1} gamma_k/k!, where gamma_0 = gamma is Euler's constant.
%e A386718 0.50044536217858002349633947881010515277510990544508...
%t A386718 With[{m = 2}, RealDigits[1 - Sum[StieltjesGamma[k]/k!, {k, 0, 2}], 10, 120][[1]]]
%Y A386718 Cf. A001620 (gamma), A082633 (-gamma_1), A086279 (-gamma_2).
%Y A386718 Cf. A153810 (m=1), A242610 (m=2), this constant (m=3).
%K A386718 nonn,cons
%O A386718 0,1
%A A386718 _Amiram Eldar_, Jul 31 2025