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 \(\phi = 0\).