`scipy.special._multiufuncs:assoc_legendre_p_all`

Signature

def assoc_legendre_p_all(n, m, z, *, branch_cut = 2, norm = False, diff_n = 0)

All associated Legendre polynomials of the first kind up to the specified degree n, order m, and all derivatives up to order diff_n.

n : int: Degree of the associated Legendre polynomials. Must have n >= 0.
m : int: Order of the associated Legendre polynomials.
z : array_like: Input value.
branch_cut : array_like of ints, optional: 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
norm : bool, optional: If True, compute the normalized associated Legendre polynomials. Default is False.
diff_n : int, optional: A non-negative integer. Compute and return all derivatives up to order diff_n. Default is 0.

: ndarray: Output shape is (diff_n + 1, n + 1, 2 * m + 1, ...). The entry at (i, j, k) corresponds to the i-th derivative, degree j, and order k for all 0 <= i <= diff_n, 0 <= j <= n, and -m <= k <= m.