Ubiquitous To Nature

Johann Heinrich Lambert (26 August 1728 – 25 September 1777) was a Swiss mathematician, physicist, philosopher and astronomer. He is best known for proving the Irrationality of π.

In mathematics, the Lambert W function, also called the omega function or product logarithm, is a set of functions, namely the branches of the inverse relation of the function f(w) = we^w where e^w is the exponential function and w is any complex number. In other words, the defining equation for W(z) is

for any complex number z.
Since the function ƒ is not injective, the relation W is multivalued (except at 0).

Multivalued.

Main branch of the Lambert W function in the complex plane.

Kompleksinė paišyba.

Lambert first considered the related Lambert's Transcendental Equation in 1758, which led to a paper by Leonhard Euler in 1783 that discussed the special case of we^w. However the inverse of we^w was first described by Pólya and Szegő in 1925. The Lambert W function was "re-discovered" every decade or so in specialized applications but its full importance was not realized until the 1990s. When it was reported that the Lambert W function provides an exact solution to the quantum-mechanical double-well Dirac delta function model for equal charges—a fundamental problem in physics—Corless and developers of the Maple Computer algebra system made a library search to find that this function was in fact ubiquitous to nature.

Пример:


следовательно,

 

Kaip tai dera su "this function was in fact ubiquitous to nature"?