The Eigenvalues of the Angular Spheroidal Wave Equation
The Eigenvalues of the Angular Spheroidal Wave Equation
复制标题
角球面波方程的特征值
DOI：
10.1002/sapm1982663217
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发表时间：
1982
影响因子：
2.7
通讯作者：
B. Guerrieri
中科院分区：
文献类型：
--
作者：
C. Hunter;B. Guerrieri
得到了角椭球波动方程的特征值λ与椭圆度参数c2之间的近似关系。虽然基于WKBJ方法和假设λ很大，但这些关系在整个复exc 2-平面上都很有用。它们在c ~ 2 = 0时是精确的，并且当c ~ 2较大时重现了λ的标准渐近公式。在c2的中间值处，它们提供复exc 2-平面中多值函数λ（c2）的平方根分支点的近似，在该点处同类的相邻特征值成对相等。这些分支点位于无限序列的扭曲圆环上。对于角波数sm = 0，.，4的前四个环，它们的精确位置已经被计算出来。
Approximate relations are obtained between the eigenvalues λ and the ellipticity parameterc2of the angular spheroidal wave equation. Although based on WKBJ methods and the assumption that λ is large, the relations are useful throughout the complexc2‐plane. They are exact atc2= 0, and reproduce the standard asymptotic formulas for λ whenc2is large. At intermediate values ofc2, they provide approximations for the square‐root branch points of the multivalued function λ(c2) in the complexc2‐plane at which adjacent eigenvalues of the same class become equal in pairs. These branch points lie on an infinite sequence of distorted circular rings. Their exact locations have been computed for the first four rings for angular wavenumbersm= 0,…,4.