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Decimal expansion of arctan(sqrt(Omega)), where Omega=LambertW(1) is the Omega constant.
2

%I #11 Apr 04 2021 01:10:54

%S 6,4,5,4,7,5,2,4,4,5,6,5,0,0,3,9,2,4,4,3,5,7,3,1,5,5,4,5,6,6,0,6,6,3,

%T 6,5,2,2,4,6,7,7,2,0,5,5,9,4,0,2,1,5,1,6,1,8,1,6,8,0,0,6,7,5,3,1,7,5,

%U 0,9,5,5,3,7,3,1,2,5,6,8,8,3,6,5,1,3,9,2,5,3,9,2,7,1,9,0

%N Decimal expansion of arctan(sqrt(Omega)), where Omega=LambertW(1) is the Omega constant.

%C The sine and the cosine of this angle appears in the values of two definite integrals that involve non-principal real branch of the Lambert W function, see A342360 and A342361.

%F Equals arctan(sqrt(LambertW(1))).

%e 0.6454752445650039244357315545660663652246772055940215161816...

%t Omega=LambertW[1]; xi=ArcTan[Sqrt[Omega]]; N[xi,120]

%o (PARI) atan(sqrt(lambertw(1)))

%Y Cf. A342360, A342361, A030178.

%K nonn,cons

%O 0,1

%A _Gleb Koloskov_, Mar 09 2021