mars.tensor.special.ellip_harm_2#
- mars.tensor.special.ellip_harm_2(h2, k2, n, p, s, **kwargs)[源代码]#
Ellipsoidal harmonic functions F^p_n(l)
These are also known as Lame functions of the second kind, and are solutions to the Lame equation:
\[(s^2 - h^2)(s^2 - k^2)F''(s) + s(2s^2 - h^2 - k^2)F'(s) + (a - q s^2)F(s) = 0\]where \(q = (n+1)n\) and \(a\) is the eigenvalue (not returned) corresponding to the solutions.
- 参数
- 返回
F – The harmonic \(F^p_n(s)\)
- 返回类型
提示
Lame functions of the second kind are related to the functions of the first kind:
\[F^p_n(s)=(2n + 1)E^p_n(s)\int_{0}^{1/s}\frac{du}{(E^p_n(1/u))^2\sqrt{(1-u^2k^2)(1-u^2h^2)}}\]