%I #9 Apr 10 2024 09:15:46

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

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

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

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

%F Equals sqrt(Pi) * Gamma(4/3) / Gamma(5/6).

%F Equals Gamma(1/3)^3 / (2^(4/3) * sqrt(3) * Pi). - _Vaclav Kotesovec_, Apr 09 2024

%F Equals A118292/2. - _Hugo Pfoertner_, Apr 09 2024

%e 1.4021821053254542611750190790502941354630222...

%t RealDigits[Sqrt[Pi] Gamma[4/3]/Gamma[5/6], 10, 104][[1]]

%t RealDigits[Gamma[1/3]^3 / (2^(4/3)*Sqrt[3]*Pi), 10, 104][[1]] (* _Vaclav Kotesovec_, Apr 09 2024 *)

%Y Decimal expansions of Integral_{x=0..1} 1 / sqrt(1 - x^k) dx: A019669 (k=2), this sequence (k=3), A085565 (k=4).

%Y Cf. A002161, A118292, A202623, A203145.

%K nonn,cons

%O 1,2

%A _Ilya Gutkovskiy_, Apr 09 2024