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:
(s2−h2)(s2−k2)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)
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