A342359 Decimal expansion of arctan(sqrt(Omega)), where Omega=LambertW(1) is the Omega constant.

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, 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, 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

Offset: 0

Author

Gleb Koloskov, Mar 09 2021

Keywords

• nonn
• cons

Comments

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.

Examples

			0.6454752445650039244357315545660663652246772055940215161816...
		

Crossrefs

Cf. A342360, A342361, A030178.

Programs

Mathematica

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

PARI

atan(sqrt(lambertw(1)))

Formula

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