A364966 Decimal expansion of the solution to exp(-x^2) = x.

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

Offset: 0

Author

Michal Paulovic, Aug 14 2023

Keywords

• nonn
• cons

Comments

Fixed point of Gaussian function.

Examples

			0.6529186404192047...
		

Links

• Eric Weisstein's World of Mathematics, Gaussian Function.
• Eric Weisstein's World of Mathematics, Lambert W-Function.
• Wikipedia, Gaussian function.
• Wikipedia, Lambert W function.
• Index entries for transcendental numbers

Crossrefs

Cf. A196515, A202498, A299624.

Programs

Maple

Digits:=105: evalf(sqrt(LambertW(2)/2));

Mathematica

RealDigits[Sqrt[ProductLog[2]/2], 10, 105][[1]]

PARI

default(realprecision, 105); sqrt(lambertw(2)/2)

Formula

Equals sqrt(LambertW(2)/2).

Equals sqrt(A196515/2).

Equals sqrt(A202498).

Equals sqrt(A299624)/2.