maxframe.tensor.special.ellip_harm_2#

maxframe.tensor.special.ellip_harm_2(h2, k2, n, p, s, **kwargs)[源代码]#

椭球谐波函数 F^p_n(l)

These are also known as Lamé functions of the second kind, and are solutions to the Lamé equation:

\[(s^2 - h^2)(s^2 - k^2)F''(s) + s(2s^2 - h^2 - k^2)F'(s) + (a - q s^2)F(s) = 0\]

其中 \(q = (n+1)n\)，\(a\) 是对应解的特征值（不返回）。

参数:

  • h2 (float) -- h**2

  • k2 (float) -- k**2；应大于 h**2

  • n (int) -- 度。

  • p (int) -- 阶数，取值范围为 [1,2n+1]。

  • s (float) -- 坐标

返回:

F -- 谐波 \(F^p_n(s)\)

返回类型:

float

参见

ellip_harm, ellip_normal

备注

Lamé functions of the second kind are related to the functions of the first kind:

\[F^p_n(s)=(2n + 1)E^p_n(s)\int_{0}^{1/s} \frac{du}{(E^p_n(1/u))^2\sqrt{(1-u^2k^2)(1-u^2h^2)}}\]