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 than- h**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: \[F^p_n(s)=(2n + 1)E^p_n(s)\int_{0}^{1/s} \frac{du}{(E^p_n(1/u))^2\sqrt{(1-u^2k^2)(1-u^2h^2)}}\]- Added 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