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# 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>

  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:
    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.

  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`.

  See also

  `assoc_legendre_p`