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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. The function is named after Johann Lambert, who considered a related problem in 1758.
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 . O mínimo global de f é dado por .
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].
a given function, is known as Poisson’s equation. The fact that there are three independent variables (x, y, and z) in (1) can be indicated by calling it the three-dimensional Laplace equation. The two-dimensional version, ∂2V ∂2V 2V 0, (2) ∇ ≡ ∂x2 + ∂y2 = also has important applications; it is a PDE for V(x,y).
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Comparing the natural log function ln(x) and the product log function W(x). 0:00 ln(x) vs. W(x)1. Solve e^x=2 & ln(2), 0:162. Solve xe^x=2 & W(2), 3:01Newton...
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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 .
