`scipy.special._ellip_harm:ellip_harm_2`

Signature

def ellip_harm_2(h2, k2, n, p, s)

Ellipsoidal harmonic functions $F_{n}^{p} (s)$ .

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 (2 s^{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.

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

F_{n}^{p} (s) = (2 n + 1) E_{n}^{p} (s) \int_{0}^{1/ s} \frac{d u}{( E _{n}^{p} ( 1/ u ) ) ^{2} ( 1 - u ^{2} k ^{2} ) ( 1 - u ^{2} h ^{2} )}

from scipy.special import ellip_harm_2
w = ellip_harm_2(5,8,2,1,10)

✓

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array(0.001)