spherical harmonic function meaning in English
球面低函数
球面调和函数
Examples
- Firstly , in spherical coordinate system , the sovp formulation for the time - harmonic electromagnetic fields of the current dipole in conductive infinite - space is derived , using reciprocity theorem and transforming relations between special functions . then , selecting appropriate coordinate system , using superposition principle , the boundary - value problem of modified magnetic vector potential on the problem of a time - harmonic current dipole in spherical conductor is solved and analytical solution is obtained . finally , by means of the addition formulas of legendre polynomial and spherical harmonics function of degree n and order 1 , the analytical solution in spherical coordinate system specially located is transformed into that in spherical coordinate system arbitrarily located
首先利用特殊函数间的转化关系和互易定理推导得到了无限大导体空间中球坐标下时谐电流元电磁场的二阶矢量位形式：然后利用叠加原理，选择合适坐标系，求解了导体球中时谐电流元的修正磁矢量位边值问题，得到了问题的解析解；最后依据不同坐标系下电磁场解的转化原理，借助勒让德多项式和n次1阶球谐函数的加法公式，将坐标系特殊安放时的电磁场解析解变换到坐标系一般安放时的解析解，给出了球内电场和球外磁场的并矢格林函数。 - The addition formula of spherical harmonics function of degree n and order 1 is derived using the relations between coordinate varieties after coordinate rotating and the property of the associated legendre polynomial . the relations among the magnetic vector potential , the modified magnetic vector potential and the second - order vector potential ( sovp ) are shown going forward one by one . it is explained that the solutions of electromagnetic fields in different coordinate systems can be transformed and an example having analytical solution is given
利用坐标旋转后球坐标变量间的关系和连带勒让德多项式的性质推导得到了n次1阶球谐函数的加法公式；以递进的方式说明磁矢量位、修正磁矢量位与二阶矢量位的关系，写出了引入二阶矢量位的过程；以时谐场矢量边值问题为例，阐明了不同坐标系下电磁场解的相互转化原理，给出了一个解析解的转化例子；在球坐标下，引入了较球矢量波函数更普遍的两类矢量函数，给出了其在球面上的正交关系。