5.7.2.10.3. scipy.special.ellip_normal¶

scipy.special.ellip_normal(h2, k2, n, p)[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 : float The normalization constant $\gamma^p_n$

See also

ellip_harm, ellip_harm_2

Notes

New in version 0.15.0.

Examples

>>>

>>> from scipy.special import ellip_normal
>>> w = ellip_normal(5,8,3,7)
>>> w
1723.38796997