A371859 - OEIS

%I #9 Apr 10 2024 09:15:37

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

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

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

%N Decimal expansion of Integral_{x=0..oo} 1 / sqrt(1 + x^5) dx.

%F Equals Gamma(3/10) * Gamma(6/5) / sqrt(Pi).

%F Equals 2^(2/5) * Gamma(1/5)^2 / (5 * phi * Gamma(2/5)), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, Apr 09 2024

%e 1.54969627774735302956219538317088212891969758...

%t RealDigits[Gamma[3/10] Gamma[6/5]/Sqrt[Pi], 10, 105][[1]]

%t RealDigits[2^(2/5) * Gamma[1/5]^2 / (5*GoldenRatio*Gamma[2/5]), 10, 105][[1]] (* _Vaclav Kotesovec_, Apr 09 2024 *)

%Y Decimal expansions of Integral_{x=0..oo} 1 / sqrt(1 + x^k) dx: A118292 (k=3), A093341 (k=4), this sequence (k=5).

%Y Cf. A001622, A087197, A340723, A352324.

%K nonn,cons

%O 1,2

%A _Ilya Gutkovskiy_, Apr 09 2024