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SciPy

This is documentation for an old release of SciPy (version 0.17.1). Read this page in the documentation of the latest stable release (version 1.15.1).

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:

(s2h2)(s2k2)F

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

Returns:

F : float

The harmonic F^p_n(s)

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