ellip_harm_2(h2, k2, n, p, s)
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.
Lame functions of the second kind are related to the functions of the first kind:
$$F^p_n(s)=(2n + 1)E^p_n(s)\int_{0}^{1/s}\frac{du}{(E^p_n(1/u))^2\sqrt{(1-u^2k^2)(1-u^2h^2)}}$$ h**2
k**2
; should be larger than h**2
Degree.
Order, can range between [1,2n+1].
Coordinate
The harmonic $F^p_n(s)$
Ellipsoidal harmonic functions F^p_n(l)
>>> from scipy.special import ellip_harm_2See :
... w = ellip_harm_2(5,8,2,1,10)
... w 0.00108056853382
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.special._ellip_harm.ellip_harm
scipy.special._ellip_harm.ellip_normal
scipy.special._ellip_harm.ellip_harm_2
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