广义椭球和球锥谐波
Generalized Ellipsoidal and Sphero-Conal Harmonics
摘要：
经典的椭球调和函数和球锥调和函数是拉普拉斯方程的多项式解，可以用拉梅多项式表示。广义椭圆和球锥调和函数是更一般的Dunkl方程的多项式解，可以用Stieltjes多项式表示。本文推广了Niven关于椭球调和函数和球锥调和函数的公式。此外，还利用广义椭球调和函数求解了Dunkl方程在椭球面上的狄利克雷问题.
英文摘要：
Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lame polynomials. Generalized ellipsoidal and sphero-conal harmonics are polynomial solutions of the more general Dunkl equation that can be expressed in terms of Stieltjes polynomials. Niven's formula connecting ellipsoidal and sphero-conal harmonics is generalized. Moreover, generalized ellipsoidal harmonics are applied to solve the Dirichlet problem for Dunkl's equation on ellipsoids.
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