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A342359
Decimal expansion of arctan(sqrt(Omega)), where Omega=LambertW(1) is the Omega constant.
2
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
0,1
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.
FORMULA
Equals arctan(sqrt(LambertW(1))).
EXAMPLE
0.6454752445650039244357315545660663652246772055940215161816...
MATHEMATICA
Omega=LambertW[1]; xi=ArcTan[Sqrt[Omega]]; N[xi, 120]
PROG
(PARI) atan(sqrt(lambertw(1)))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Gleb Koloskov, Mar 09 2021
STATUS
approved