关于汤姆森在球调和函数方面的工作之历史探析

History Analysis of Thomson’s Work on Spherical Harmonics

汤姆森在球调和函数方面的工作是位势理论中的重要部分。在拉普拉斯、勒让德、傅里叶等人势理论及热的解析理论工作基础上,汤姆森是第一位定义球调和分析,给出球调和函数概念及其性质特征,并将任意函数表示成球面调和函数的线性组合。为拉普拉斯方程求解提供了新的有效方法,并被应用于一系列数学物理问题中。本文基于原始文献及研究文献,对汤姆森在球调和函数方面的数学工作进行探析,追溯其创新方法的思想起源及物理应用过程。

Thomson’s work on spherical harmonics is an important part in potential theory. On thebasis of potential theory work of Laplace and Legendre, and Fourier’s thermal analysis theory,Thomson was the the first given the definition of the spherical analysis, spherical harmonics and its property, and expression the arbitrary function as a linear combination of surface spherical harmonics. In which the innovative mathematical way not only provide new effective method for solution of Laplace equation but applied in a series of physical problems.Based on original literatures, this paper aim to analyze Thomson’s work on spherical harmonics, trace origin of its thought and application.