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.
翻译：在本文中,我们研究了角形人造波波方程式及其一般化的天体值,Coulomb 人造波方程式。相关的差分系统和各种花粉溶液之间连接系数的公式产生了一个完整的函数,其零正好是库伦姆人造波方程式的天体值。整个函数可以通过一个具有任意精确性和低计算成本的重现公式来计算。最后,一个人获得了一种易于使用的计算人造天体元值和相应的天体元值的方法。
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