scipy.special.assoc_legendre_p_all#

scipy.special.assoc_legendre_p_all(n, m, z, *, branch_cut=2, norm=False, diff_n=0) = <scipy.special._multiufuncs.MultiUFunc object>[source]#

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

Parameters:

nint: Degree of the associated Legendre polynomials. Must have n >= 0.
mint: Order of the associated Legendre polynomials.
zarray_like: Input value.
branch_cutarray_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
normbool, optional: If True, compute the normalized associated Legendre polynomials. Default is False.
diff_nint, optional: A non-negative integer. Compute and return all derivatives up to order diff_n. Default is 0.

Returns:

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.