# scipy.special.ellip_harm_2¶

scipy.special.ellip_harm_2(h2, k2, n, p, s)[source]

Ellipsoidal harmonic functions F^p_n(l)

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.

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]. s : float Coordinate F : float The harmonic $$F^p_n(s)$$

See also

Notes

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

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

New in version 0.15.0.

Examples

>>> from scipy.special import ellip_harm_2
>>> w = ellip_harm_2(5,8,2,1,10)
>>> w
0.00108056853382


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