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单词 Product log
释义

Product log

中文百科

朗伯W函数 Lambert W function

(重定向自Product log)
W0(x)的图像,−1/e ≤ x ≤ 4
复平面上的朗伯W函数
LambertWAbs.png

朗伯W函数英语:Lambert W function,又称为欧米加函数乘积对数),是f(w) = we的反函数,其中e是指数函数,w是任意复数。对于任何复数z,都有:

由于函数f不是单射,因此函数W是多值的(除了0以外)。如果我们把x限制为实数,并要求w是实数,那幺函数仅对于x ≥ −1/e有定义,在(−1/e, 0)内是多值的;如果加上w ≥ −1的限制,则定义了一个单值函数W0(x)(见图)。我们有W0(0) = 0,W0(−1/e) = −1。而在[−1/e, 0)内的w ≤ −1分支,则记为W−1(x),从W−1(−1/e) = −1递减为W−1(0) = −∞。

英语百科

Lambert W function 朗伯W函数

(重定向自Product log)
The graph of W(x) for W > −4 and x < 6. The upper branch with W ≥ −1 is the function W0 (principal branch), the lower branch with W ≤ −1 is the function W−1.
Main branch of the Lambert W function in the complex plane.  Note the branch cut along the negative real axis, ending at −1/e. In this picture, the hue of a point z is determined by the argument of W(z) and the brightness by the absolute value of W(z).

In mathematics, the Lambert W function, also called the omega function or product logarithm, is a set of functions, namely the branches of the inverse relation of the function f(z) = ze where e is the exponential function and z is any complex number. In other words

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更新时间:2025/6/21 6:27:26