Derivatives of addition theorems for Legendre functions
Derivatives of addition theorems for Legendre functions
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DOI：
10.1017/s0334270000007670
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发表时间：
1995-10
期刊：
影响因子：
--
通讯作者：
D. Winch;P. Roberts
中科院分区：
文献类型：
--
作者：
D. Winch;P. Roberts
勒让德多项式加法定理的微分给出了相关勒让德函数的各种导数乘积的m阶和的结果。同样的方法也适用于向量和张量球谐函数的相应加法定理。结果也给出了切比雪夫多项式的第二类，对应于“自旋加权”相关的勒让德函数，用于旋转分布的研究。
Abstract Differentiation of the well-known addition theorem for Legendre polynomials produces results for sums over order m of products of various derivatives of associated Legendre functions. The same method is applied to the corresponding addition theorems for vector and tensor spherical harmonics. Results are also given for Chebyshev polynomials of the second kind, corresponding to ‘spin-weighted’ associated Legendre functions, as used in studies of distributions of rotations.