Lambert W函数与黑体辐射的双值问题

The Dual-Valued Problem of Lambert’s W Function and Blackbody Radiation

摘要: 本文介绍了Lambert W函数和它的性质，特别是函数的定义域在(−1/e, 0)范围时，函数是双值函数。在黑体辐射的求解中，需要应用到Lambert W函数，但在物理计算中，没有考虑该函数的双值问题，只求解出一个解，而实际有两个解。在黑体辐射求解中应用了4次Lambert W函数，均有一个函数值小于−1的情况，分别是−2，−3，−4，−5。Lambert W函数的性质在黑体辐射的计算中被忽视了。

Abstract: This paper introduces the Lambert W function and its properties, particularly its bivalued nature when the domain is (−1/e, 0). The Lambert W function is required for solving blackbody radiation, but in physical calculations, its bivalued nature is often overlooked, resulting in only one solution when two solutions are actually found. In the blackbody radiation calculation, the Lambert W function was applied four times, and in each case, one function value was less than −1: −2, −3, −4, and −5. The properties of the Lambert W function have been neglected in blackbody radiation calculations.