scipy.special.assoc_legendre_p#
- scipy.special.assoc_legendre_p(n, m, z, *, branch_cut=2, norm=False, diff_n=0) = <scipy.special._multiufuncs.MultiUFunc object>[source]#
- Associated Legendre polynomial of the first kind. - Parameters:
- nArrayLike[int]
- Degree of the associated Legendre polynomial. Must have - n >= 0.
- mArrayLike[int]
- order of the associated Legendre polynomial. 
- zArrayLike[float | complex]
- Input value. 
- branch_cutOptional[ArrayLike[int]]
- Selects branch cut. Must be 2 (default) or 3. 2: cut on the real axis - |z| > 13: cut on the real axis- -1 < z < 1
- normOptional[bool]
- If - True, compute the normalized associated Legendre polynomial. Default is- False.
- 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]
- Associated Legendre polynomial with - diff_nderivatives.
 
 - Notes - The normalized counterpart of an (unnormalized) associated Legendre polynomial has the additional factor \[\sqrt{\frac{(2 n + 1) (n - m)!}{2 (n + m)!}}\]