球面谐和函数Y_(lm)(θ,φ)的降阶表达式

A Lowering-order Expression of Spherical Harmonic Function

本文给出连带勒让特函数P_1(x)的二个新递推公式,由它只需经简单的代数运算就可从一阶连带勒让特函数P_1~0(x)与P_1~1(x)逐次求得任意高阶连带勒让特函数。并在这两个新公式基础上导得球面谐和函数Y_l(θ,φ)的降阶表达式。

Two new recurrence formulas of associated Legendre function P_(?)^(?)(x) are given, using these formulas, we can extract ang higher order associated Legendre function from P_1~0(x) and P_1~1(x). A new lowering-order expression of spherical harmonic function is also derived from these two new recurrence formulas.