A371859 Decimal expansion of Integral_{x=0..oo} 1 / sqrt(1 + x^5) dx.

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, 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, 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

Offset: 1

Author

Ilya Gutkovskiy, Apr 09 2024

Keywords

• nonn
• cons

Examples

			1.54969627774735302956219538317088212891969758...
		

Crossrefs

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

Cf. A001622, A087197, A340723, A352324.

Programs

Mathematica

RealDigits[Gamma[3/10] Gamma[6/5]/Sqrt[Pi], 10, 105][[1]]
RealDigits[2^(2/5) * Gamma[1/5]^2 / (5*GoldenRatio*Gamma[2/5]), 10, 105][[1]] (* Vaclav Kotesovec, Apr 09 2024 *)

Formula

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

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