A371861 Decimal expansion of Integral_{x=0..1} sqrt(1 - x^3) dx.

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, 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, 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

Offset: 0

Author

Ilya Gutkovskiy, Apr 09 2024

Keywords

• nonn
• cons

Examples

			0.8413092631952725567050114474301764812778...
		

Crossrefs

Decimal expansions of Integral_{x=0..1} sqrt(1 - x^k) dx: A003881 (k=2), this sequence (k=3), A225119 (k=4).

Cf. A002161, A073005, A118292, A203131.

Programs

Mathematica

RealDigits[Sqrt[Pi] Gamma[1/3]/(6 Gamma[11/6]), 10, 103][[1]]
RealDigits[Sqrt[3] * Gamma[1/3]^3 / (5*Pi*2^(4/3)), 10, 103][[1]] (* Vaclav Kotesovec, Apr 09 2024 *)

PARI

intnum(x=0, 1, sqrt(1 - x^3)) \\ Michel Marcus, Apr 10 2024

Formula

Equals sqrt(Pi) * Gamma(1/3) / (6 * Gamma(11/6)).

Equals sqrt(3) * Gamma(1/3)^3 / (5*Pi*2^(4/3)). - Vaclav Kotesovec, Apr 09 2024

Equals 3*A118292/10. - Hugo Pfoertner, Apr 09 2024