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>

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| > 1 3: 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_n derivatives.

Notes

The normalized counterpart of an (unnormalized) associated Legendre polynomial has the additional factor

\[\sqrt{\frac{(2 n + 1) (n - m)!}{2 (n + m)!}}\]