论文标题
角度和库仑球形方程的特征值计算
Computation of the eigenvalues for the angular and Coulomb spheroidal wave equation
论文作者
论文摘要
在本文中，我们研究了角球波方程的特征值及其概括，即库仑球波方程。相关的差分系统和一个用于各种浮雕溶液之间连接系数的公式产生了整个函数，其零是库仑球形波方程的特征值。可以通过任意准确性和低计算成本的复发公式来计算整个功能。最后，人们获得了一种易于使用的方法来计算球形特征值和相应的特征功能。
In this paper we study the eigenvalues of the angular spheroidal wave equation and its generalization, the Coulomb spheroidal wave equation. An associated differential system and a formula for the connection coefficients between the various Floquet solutions give rise to an entire function whose zeros are exactly the eigenvalues of the Coulomb spheroidal wave equation. This entire function can be calculated by means of a recurrence formula with arbitrary accuracy and low computational cost. Finally, one obtains an easy-to-use method for computing spheroidal eigenvalues and the corresponding eigenfunctions.
