Tīmeklis朗伯W函數(英語: Lambert W function ,又稱為歐米加函數或乘積對數),是f(w) = we w 的反函數,其中e w 是指數函數,w是任意複數。 對於任何複數z,都有: = (). 由於函數f不是單射,因此函數W是多值的(除了0以外)。 如果我們把x限制為實數,並要求w是實數,那麼函數僅對於x ≥ −1/e有定義,在(−1/e ...
朗伯 W函数(Lambert W Function) - 知乎 - 知乎专栏
Tīmeklis我们习惯将蓝色部分书写作 W(x) ,而将红色部分书写作 W_{-1}(x). 下面我们介绍朗伯函数的求导方式、泰勒级数及一些需要注意的地方。 我们知道因为朗伯函数被定义为 … TīmeklisNotes. All branches are supported by lambertw:. lambertw(z) gives the principal solution (branch 0) lambertw(z, k) gives the solution on branch k The Lambert W … ein state of california
ランベルトの W 関数 - MATLAB lambertw - MathWorks 日本
Tīmeklislambertw是matlab的一个函数 意思是x*e^x=W; x=lambertw(W) 其实你只要将这个结果再次放入Command 窗口 就可以运行处结果了 例如: >> -lambertw(0, -5/22) ans = … There are countably many branches of the W function, denoted by Wk(z), for integer k; W0(z) being the main (or principal) branch. W0(z) is defined for all complex numbers z while Wk(z) with k ≠ 0 is defined for all non-zero z. We have W0(0) = 0 and Wk(z) = −∞ for all k ≠ 0. The branch point for … Skatīt vairāk 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 , where w is any complex number and … Skatīt vairāk Lambert first considered the related Lambert's Transcendental Equation in 1758, which led to an article by Leonhard Euler in 1783 that discussed the special case of we . Skatīt vairāk The Taylor series of W0 around 0 can be found using the Lagrange inversion theorem and is given by The Skatīt vairāk The principal branch of the Lambert function can be represented by a proper integral, due to Poisson: On the wider … Skatīt vairāk The Lambert W function is named after Johann Heinrich Lambert. The principal branch W0 is denoted Wp in the Digital Library of Mathematical Functions, and the branch W−1 is denoted Wm there. The notation convention chosen here (with W0 and W−1) … Skatīt vairāk Derivative By implicit differentiation, one can show that all branches of W satisfy the differential equation Skatīt vairāk A few identities follow from the definition: Note that, since f(x) = xe is not injective, it does not always … Skatīt vairāk TīmeklisThe principal branch and the pair of branches LambertW(-1, x) and LambertW(1, x) share an order 2 branch point at -exp(-1). The branch cut dividing these branches is … fonton industrial