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

1,2

Links

Table of n, a(n) for n=1..105.

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.

Example

1.3207304008696366654886148277807262075232447951825960706678785858663...

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 *)

Crossrefs

Cf. A229191.

Sequence in context: A262294 A080779 A355090 * A309680 A010604 A067585

Adjacent sequences: A319827 A319828 A319829 * A319831 A319832 A319833

Keyword

nonn,cons

Author

Sam Coutteau, Sep 28 2018

Extensions

More terms from Vaclav Kotesovec, Jan 15 2019

Status

approved