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 A254135 #13 Aug 06 2024 09:28:05 %S A254135 6,9,2,6,6,0,8,1,5,1,5,2,6,4,7,5,0,6,5,0,9,4,3,1,1,8,5,8,8,4,2,7,2,4, %T A254135 5,8,4,6,7,1,3,4,8,3,2,8,0,7,6,6,8,8,4,2,5,8,0,7,2,0,4,5,6,9,7,1,4,9, %U A254135 0,6,3,0,2,1,6,3,0,0,7,0,5,2,1,4,3,3,9,1,1,7,7,2,8,2,0,4,4,2,8,6,8,3,9 %N A254135 Decimal expansion of Lamb's integral K_2. %H A254135 D. H. Bailey, J. M. Borwein, and R. E. Crandall, <a href="https://citeseerx.ist.psu.edu/pdf/7f8e05b56fe9a987cf8f50f5f71414954bd94c1e">Advances in the theory of box integrals</a> (2010) p. 18. %H A254135 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/InverseTangentIntegral.html">Inverse Tangent Integral</a>. %F A254135 K_2 = integral_[0..Pi/4] sqrt(1 + sec(x)^2)*arctan(1/sqrt(1 + sec(x)^2)) dx. %F A254135 K_2 = (1/2)*Ti_2(-2 + sqrt(3)) + (Pi/8)*log(2 + sqrt(3)) + Pi^2/32, where Ti_2 is Lewin's arctan integral, Ti_2(x) = (i/2)*(Li_2(-i*x) - Li_2(i*x)). %e A254135 0.69266081515264750650943118588427245846713483280766884258... %p A254135 evalf(int(sqrt(1 + sec(x)^2)*arctan(1/sqrt(1 + sec(x)^2)), x=0..Pi/4), 120); # _Vaclav Kotesovec_, Jan 26 2015 %t A254135 Ti2[x_] := (I/2)* (PolyLog[2, -I *x] - PolyLog[2, I *x]); K2 = (1/2)*Ti2[-2 + Sqrt[3]] + (Pi/8)*Log[2 + Sqrt[3]] + Pi^2/32 // Re; RealDigits[K2, 10, 103] // First %Y A254135 Cf. A244920, A244921, A244922, A254133, A254134. %K A254135 nonn,cons,easy %O A254135 0,1 %A A254135 _Jean-François Alcover_, Jan 26 2015