scipy.special.sph_legendre_p#
- scipy.special.sph_legendre_p(n, m, theta, *, diff_n=0) = <scipy.special._multiufuncs.MultiUFunc object>[source]#
- Spherical Legendre polynomial of the first kind. - Parameters:
- nArrayLike[int]
- Degree of the spherical Legendre polynomial. Must have - n >= 0.
- mArrayLike[int]
- Order of the spherical Legendre polynomial. 
- thetaArrayLike[float]
- Input value. 
- diff_nOptional[int]
- A non-negative integer. Compute and return all derivatives up to order - diff_n. Default is 0.
 
- Returns:
- pndarray or tuple[ndarray]
- Spherical Legendre polynomial with - diff_nderivatives.
 
 - Notes - The spherical counterpart of an (unnormalized) associated Legendre polynomial has the additional factor \[\sqrt{\frac{(2 n + 1) (n - m)!}{4 \pi (n + m)!}}\]- It is the same as the spherical harmonic \(Y_{n}^{m}(\theta, \phi)\) with \(\phi = 0\).