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:
- h2float
h**2
- k2float
k**2
; should be larger thanh**2
- nint
Degree.
- pint
Order, can range between [1,2n+1].
- sfloat
Coordinate
- Returns:
- Ffloat
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