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In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse relation of the function f(w) = we w, where w is any complex number and e w is the exponential function.
A função W de Lambert, devida ao matemático suíço Johann Heinrich Lambert, é a função transcendental que resolve a equação em y: = Ou seja, se y = W(x), então y resolve y e y = x.
The Lambert W-function, also called the omega function, is the inverse function of f(W)=We^W. (1) The plot above shows the function along the real axis. The principal value of the Lambert W-function is implemented in the Wolfram Language as ProductLog[z].
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A função W de Lambert, devida ao matemático suíço Johann Heinrich Lambert, é a função transcendental que resolve a equação em y: Ou seja, se y = W (x), então y resolve y ey = x. A função W de Lambert pode ser vista como a função inversa de , uma função decrescente para e crescente para .
The Lambert W -function W ( z) is the solution of the equation. On the z -interval [ 0, ∞) there is one real solution, and it is nonnegative and increasing. On the z -interval ( − e − 1, 0) there are two real solutions, one increasing and the other decreasing.
The Lambert W function is used in mathematics to solve equations in which the unknown appears both outside and inside an exponential function or a logarithm, such as 3x + 2 = ex or x = ln (4x). Such equations cannot otherwise, except in special cases, be solved explicitly in terms of algebraic operations, exponentials and logarithms. Contents.
