A277069 Decimal expansion of the real part of the root of the function x^y = y.

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

Offset: 2

Author

David D. Acker, Sep 27 2016

Keywords

• nonn
• cons

Comments

This value is negative.

It is not known if this number has a closed form.

This root occurs on the real component of the function x^y = y for x values which are all real.

Examples

			-99.1120147991877404695252398904774418725997764195131575672373129...
		

Crossrefs

Cf. A277067.

Programs

Mathematica

FindRoot[Re[-ProductLog[-Log[x]]/Log[x]], {x, -100, -99}, WorkingPrecision -> 261]

Formula

Original fixed point function is of the form: x^y = y. When solved for y: y = -ProductLog(-log(x))/log(x).