缔合勒让德函数的解析表达式研究

把任意n阶m次缔合勒让德函数Pmn(cosθ)表示为系数E(k)与角度(n－2k)θ的正弦或余弦乘积之和，k的取值范围是0到int[n/2]。当缔合勒让德函数的次小于等于2时，其系数E(k)可利用P0n(cosθ)展开式的系数来表示|否则，其将是几个数组的线性组合。本文给出的解析表达式有助于理解勒让德函数的特性及证明。

Restudy on Analytical Expression of Associated Legendre Function

In this paper, the associated Legendre function, with arbitrary order n and degree m Pmn(cosθ), is represented as the product sum of the coefficient E(k) and the angle (n－2k)θ′ss sine or cosine. The available value range of k is from 0 to int[n/2]. 〖JP2〗When the degree m is less than or equal to 2, E(k) can be expressed by the coefficient of P0n(cosθ) expansion. Otherwise, it will be a linear combination of several arrays. The given analytical expression not only helps to understand the Legendre function’s characteristics and property proof, but also can simplify its application in the related technical field.