Slater型函数Guseinov重排单值域加法定理的数学性质
On the Mathematical Nature of Guseinov's Rearranged One-Range Addition Theorems for Slater-Type Functions
摘要：
Guseinov从Slater型函数的单值域加法定理出发，构造了Slater型函数的加法定理，该加法定理是基于广义Laguerre多项式的完备正交函数的展开式，具有公共的标度参数和积分主量子数.这是通过将完全和正交的拉盖尔型函数表示为斯莱特型函数的有限线性组合，并通过重新排列嵌套求和的顺序来实现的。本质上，这对应于拉盖尔展开式的变换，拉盖尔展开式通常只在均值上收敛，而幂级数则逐点收敛。这样的转换不一定是合法的，这篇文章详细讨论了截断展开式和导致没有截断的无穷级数之间的区别
英文摘要：
Starting from one-range addition theorems for Slater-type functions, which are expansion in terms of complete and orthonormal functions based on the generalized Laguerre polynomials, Guseinov constructed addition theorems that are expansions in terms of Slater-type functions with a common scaling parameter and integral principal quantum numbers. This was accomplished by expressing the complete and orthonormal Laguerre-type functions as finite linear combinations of Slater-type functions and by rearranging the order of the nested summations. Essentially, this corresponds to the transformation of a Laguerre expansion, which in general only converges in the mean, to a power series, which converges pointwise. Such a transformation is not necessarily legitimate, and this contribution discusses in detail the difference between truncated expansions and the infinite series that result in the absence of truncation
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
