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 A254979 #34 Feb 16 2025 08:33:24
%S A254979 1,1,2,1,8,9,9,6,1,8,7,1,5,8,6,0,9,7,7,3,5,1,6,1,5,1,7,5,5,6,7,5,4,2,
%T A254979 7,0,9,2,0,0,8,0,7,9,5,6,4,3,9,5,4,5,8,3,0,8,3,6,7,9,2,4,6,6,9,1,6,4,
%U A254979 0,3,5,4,8,6,0,6,9,1,5,3,4,9,0,2,4,6,7,3,1,4,5,5,7,8,6,3,7,6,4,4,9,7,6,3,4
%N A254979 Decimal expansion of the mean Euclidean distance from a point in a unit 4D cube to a given vertex of the cube (named B_4(1) in Bailey's paper).
%C A254979 Also, decimal expansion of twice the expected distance from a randomly selected point in the unit 4D cube to the center. - _Amiram Eldar_, Jun 04 2023
%H A254979 D. H. Bailey, J. M. Borwein and R. E. Crandall, <a href="https://doi.org/10.1016/j.cam.2006.06.010">Box Integrals</a>, J. Comp. Appl. Math., Vol. 206, No. 1 (2007), pp. 196-208.
%H A254979 D. H. Bailey, J. M. Borwein, and R. E. Crandall, <a href="http://dx.doi.org/10.1090/S0025-5718-10-02338-0">Advances in the theory of box integrals</a>, Math. Comp. 79 (271) (2010) 1839-1866, Table 2.
%H A254979 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/InverseTangentIntegral.html">Inverse Tangent Integral</a>.
%H A254979 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Polylogarithm.html">Polylogarithm</a>.
%H A254979 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BoxIntegral.html">Box Integral</a>.
%F A254979 Equals B_4(1) = 2/5 - Catalan/10 + (3/10)*Ti_2(3-2*sqrt(2)) + log(3) - (7*sqrt(2)/10) * arctan(1/sqrt(8)), where Ti_2(x) = (i/2)*(polylog(2, -i*x) - polylog(2, i*x)) (Ti_2 is the inverse tangent integral function).
%e A254979 1.12189961871586097735161517556754270920080795643954583...
%t A254979 Ti2[x_] := (I/2)*(PolyLog[2, -I*x] - PolyLog[2, I*x]); B4[1] = 2/5 - Catalan/10 + (3/10)*Ti2[3 - 2*Sqrt[2]] + Log[3] - (7*Sqrt[2]/10)*ArcTan[1/Sqrt[8]] // Re; RealDigits[B4[1], 10, 105] // First
%t A254979 N[Integrate[1/u^2 - Pi^2*Erf[u]^4/(16*u^6), {u, 0, Infinity}]/Sqrt[Pi], 50] (* _Vaclav Kotesovec_, Aug 13 2019 *)
%o A254979 (Python)
%o A254979 from mpmath import *
%o A254979 mp.dps=106
%o A254979 x=3 - 2*sqrt(2)
%o A254979 Ti2x=(j/2)*(polylog(2, -j*x) - polylog(2, j*x))
%o A254979 C = 2/5 - catalan/10 + (3/10)*Ti2x + log(3) - (7*sqrt(2)/10)*atan(1/sqrt(8))
%o A254979 print([int(n) for n in str(C.real).replace('.', '')]) # _Indranil Ghosh_, Jul 04 2017
%Y A254979 Cf. A117653, A117654, A244920, A254968.
%Y A254979 Analogous constants: A244921 (square), A130590 (cube).
%K A254979 nonn,cons,easy
%O A254979 1,3
%A A254979 _Jean-François Alcover_, Feb 11 2015
%E A254979 Name corrected by _Amiram Eldar_, Jun 04 2023