mars.tensor.special.ellip_normal#

mars.tensor.special.ellip_normal(h2, k2, n, p, **kwargs)[source]#

Ellipsoidal harmonic normalization constants gamma^p_n

The normalization constant is defined as

\[\gamma^p_n=8\int_{0}^{h}dx\int_{h}^{k}dy\frac{(y^2-x^2)(E^p_n(y)E^p_n(x))^2}{\sqrt((k^2-y^2)(y^2-h^2)(h^2-x^2)(k^2-x^2)}\]
Parameters

  • h2 (float) – h**2

  • k2 (float) – k**2; should be larger than h**2

  • n (int) – Degree.

  • p (int) – Order, can range between [1,2n+1].

Returns

gamma – The normalization constant \(\gamma^p_n\)

Return type

float

See also

ellip_harm, ellip_harm_2