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 A365317 #27 Mar 28 2025 02:10:26 %S A365317 3,7,9,8,0,4,8,9,1,7,9,1,3,9,0,1,5,6,9,9,1,7,9,7,0,5,1,3,4,1,6,2,3,6, %T A365317 2,7,6,8,9,1,2,7,0,3,5,1,9,2,7,4,2,8,5,2,0,3,5,8,9,1,9,7,6,9,7,7,8,4, %U A365317 6,7,4,7,8,3,5,8,6,1,4,4,5,0,8,4,6,7,1,7,8,3,0,8,3,1,8,6,3,2,2,0,9,8,7,9,0,9 %N A365317 Decimal expansion of real part of Gamma(exp(i*Pi/3)). %C A365317 For imaginary part of Gamma(exp(i*Pi/3)) see A365318. %C A365317 For abs(Gamma(exp(i*Pi/3))) see A365319. %H A365317 Juan Arias de Reyna and Jan van de Lune, 2013, <a href="https://arxiv.org/abs/1305.3844">On the exact location of the non-trivial zeros of Riemann's zeta function</a>, arXiv:1305.3844 [math.NT], 2013, formula (4). %H A365317 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Riemann-SiegelFunctions.html">Riemann-Siegel Functions</a>. %H A365317 Wikipedia, <a href="https://en.wikipedia.org/wiki/Riemann%E2%80%93Siegel_theta_function">Riemann-Siegel theta function</a>. %F A365317 Equals sqrt(Pi*sech(Pi*sqrt(3)/2))*cos(2*theta(sqrt(3)/2)+(sqrt(3)/2)*log(2*Pi)+arctan(tanh(Pi*sqrt(3)/4))) where theta is Riemann-Siegel theta function. %e A365317 0.37980489179139... %t A365317 RealDigits[Re[Gamma[Cos[Pi/3] + I Sin[Pi/3]]], 10, 106][[1]] %t A365317 (* or *) %t A365317 RealDigits[Sqrt[Pi/Cosh[Pi Sqrt[3]/2]] Cos[2 RiemannSiegelTheta[Sqrt[3]/2] + ArcTan[Tanh[Pi Sqrt[3]/4]] + Sqrt[3] Log[2 Pi]/2], 10, 106][[1]] %o A365317 (PARI) real(gamma(exp(I*Pi/3))) \\ _Michel Marcus_, Sep 01 2023 %Y A365317 Cf. A212877, A212878, A212879, A212880, A365318, A365319. %K A365317 nonn,cons %O A365317 0,1 %A A365317 _Artur Jasinski_, Sep 01 2023