Lambert W函数与指数和线性函数组合方程的求解
Solving Equations Combining Exponential and Linear Functions by Lambert W Function
DOI: 10.12677/pm.2026.161027, PDF,    科研立项经费支持
作者: 王广福：季华实验室，广东 佛山；中国煤炭科学研究院矿山人工智能研究所，北京；盛选禹*：季华实验室，广东 佛山；董盛卉：广东外语外贸大学日语语音文化学院，广东 广州
关键词: Lambert W函数；指数函数；线性函数；函数导数；Lambert W Function； Exponential Function； Linear Function； Function Derivative
摘要: Lambert W函数形式为 W( x )=x e x ，是一类特殊函数，x在[−1/e, 0]区间内，W(x)有双值，x在[0, +∞)区间内，W(x)是单值。利用Lambert W函数，本文对于指数和线性函数的多个组合方程进行求解，并得出多种组合方程的标准解。
Abstract: The Lambert W function, in the form W( x )=x e x , is a special class of functions. W(x) has two values in the interval [−1/e, 0], and is single-valued in the interval [0, +∞). Using the Lambert W function, this paper solves multiple combined equations of exponential and linear functions, and derives standard solutions for various combined equations.
文章引用：王广福, 盛选禹, 董盛卉. Lambert W函数与指数和线性函数组合方程的求解[J]. 理论数学, 2026, 16(1): 247-255. https://doi.org/10.12677/pm.2026.161027

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