%I #18 Aug 06 2024 05:59:18
%S 1,9,9,5,4,8,1,2,9,1,3,4,7,6,0,2,8,1,5,0,5,6,9,1,1,7,1,4,7,5,4,3,2,6,
%T 9,8,3,2,2,3,1,2,3,9,4,0,8,7,0,9,4,3,5,5,1,4,8,0,9,7,1,6,6,5,6,9,5,9,
%U 0,8,8,8,9,4,0,3,3,9,2,0,1,2,5,3,7,8,3
%N Decimal expansion of (gamma + log(2)) * Pi / 2.
%C Shamos has incorrect integral expression for this constant.
%D I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, Academic Press (1979), Eq. (4.421.1).
%H Michael I. Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">Shamos's catalog of the real numbers</a> (2011).
%F Equals -Integral_{x=0..infinity} log(x) * sin(2*x) / x dx.
%F More generally, Integral_{x=0..infinity} log(x) * sin(k*x) / x dx = -(Pi/2) * (gamma+log(k)).
%e 1.995481291347602815056911714754326983223123940...
%p evalf((gamma+log(2))*Pi/2, 140); # _Alois P. Heinz_, Aug 20 2021
%t RealDigits[(EulerGamma + Log[2])*Pi/2, 10, 120][[1]] (* _Amiram Eldar_, Jun 07 2023 *)
%o (PARI) (Euler + log(2))*Pi/2 \\ _Michel Marcus_, Aug 20 2021
%Y Cf. A001620.
%K nonn,cons
%O 1,2
%A _Sean A. Irvine_, Aug 20 2021