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Lambert W function. The Lambert W function W (z) is defined as the inverse function of w * exp(w). In other words, the value of W(z) is such that z = W(z) * exp(W(z)) for any complex number z. The Lambert W function is a multivalued function with infinitely many branches. Each branch gives a separate solution of the equation z = w exp(w).
27 de nov. de 2020 · This function is defined implicitly as the inverse of the nonlinear transcendental equation. W(z)eW(z) = z W ( z) e W ( z) = z. Since the function inverts this relation, one can immediately write. W−1(z) = zez W − 1 ( z) = z e z. The Lambert function has an infinite number of complex branches, like the complex natural logarithm that ...
28 de mai. de 2024 · We will discuss how to use the Lambert W function to help us solve more equations, such as x^x=2 and x^2=2^x. We will also do calculus with the Lamber W func...
13 de ago. de 2020 · The Lambert W function is the multi-valued inverse of the holomorphic function \(E :z\mapsto z\exp z\).It is well known that W has very many applications throughout the sciences, and even though there are very few explicit formulae available for any of the branches of W, its usefulness has grown enormously in recent times due to our ability to compute specific values of W.
7 de jun. de 2016 · 朗博函数简介. 朗博W函数 (Lambert W Function)，又称欧米伽函数或乘积对数函数，是复变函数 f(x) = x ⋅ exp(x) 的反函数．如果我们把朗博函数的定义域限制在 [− 1 e, + ∞) 上，取其在 [ − 1, + ∞) 上的函数值，那么就定义了一个单调递增的函数 W(x) ；同时将定义域在 ...
The Lambert W function is defined to be the multivalued inverse of the function w → we w. It has many applications in pure and applied mathematics, some of which are briefly described here. We present a new discussion of the complex branches of W, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating ...
