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%I #14 Apr 10 2024 03:58:22
%S 8,4,1,3,0,9,2,6,3,1,9,5,2,7,2,5,5,6,7,0,5,0,1,1,4,4,7,4,3,0,1,7,6,4,
%T 8,1,2,7,7,8,1,3,3,2,3,2,5,4,3,9,1,6,5,7,7,0,9,1,9,6,3,9,2,2,4,5,7,7,
%U 0,8,5,9,5,8,9,0,8,1,9,7,7,6,4,2,5,1,1,3,5,9,8,9,1,0,1,4,8,7,0,8,2,3,3
%N Decimal expansion of Integral_{x=0..1} sqrt(1 - x^3) dx.
%F Equals sqrt(Pi) * Gamma(1/3) / (6 * Gamma(11/6)).
%F Equals sqrt(3) * Gamma(1/3)^3 / (5*Pi*2^(4/3)). - _Vaclav Kotesovec_, Apr 09 2024
%F Equals 3*A118292/10. - _Hugo Pfoertner_, Apr 09 2024
%e 0.8413092631952725567050114474301764812778...
%t RealDigits[Sqrt[Pi] Gamma[1/3]/(6 Gamma[11/6]), 10, 103][[1]]
%t RealDigits[Sqrt[3] * Gamma[1/3]^3 / (5*Pi*2^(4/3)), 10, 103][[1]] (* _Vaclav Kotesovec_, Apr 09 2024 *)
%o (PARI) intnum(x=0, 1, sqrt(1 - x^3)) \\ _Michel Marcus_, Apr 10 2024
%Y Decimal expansions of Integral_{x=0..1} sqrt(1 - x^k) dx: A003881 (k=2), this sequence (k=3), A225119 (k=4).
%Y Cf. A002161, A073005, A118292, A203131.
%K nonn,cons
%O 0,1
%A _Ilya Gutkovskiy_, Apr 09 2024
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