A319830 Decimal expansion of Integral_{0..oo} (x^(1/x-x)) dx.

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

Offset: 1

Author

Sam Coutteau, Sep 28 2018

Keywords

• nonn
• cons

Examples

			1.3207304008696366654886148277807262075232447951825960706678785858663...
		

Crossrefs

Cf. A229191.

Programs

Maple

evalf(Int(x^(1/x-x), x = 0..infinity), 120);

Mathematica

RealDigits[NIntegrate[x^(1/x - x), {x, 0, Infinity}, WorkingPrecision -> 120]][[1]] (* Vaclav Kotesovec, Jan 15 2019 *)

Formula

Equals Integral_{0..oo} (x^(1/x-x)) dx (definition).

Equals Integral_{0..1} (x^(1/x-x) * (1 + 1/x^2) ) dx.

Equals Integral_{0..oo} ( (x + sqrt(x^2 + 4))/2 )^(-x) dx.

Extensions

More terms from Vaclav Kotesovec, Jan 15 2019