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# scipy.special.sph_harm_y_all

scipy.special.sph_harm_y_all(n, m, theta, phi, *, diff_n=0) = <scipy.special._multiufuncs.MultiUFunc object>

  All spherical harmonics up to the specified degree n, order m, and all derivatives up to order diff_n.

  Parameters:
    n int

      Degree of the harmonics. Must have `n >= 0`. This is often denoted by `l` (lower case L) in descriptions of spherical harmonics.

    m int

      Order of the harmonics.

    theta array_like

      Polar (colatitudinal) coordinate; must be in `[0, pi]`.

    phi array_like

      Azimuthal (longitudinal) coordinate; must be in `[0, 2*pi]`.

    diff_n int, optional

      A non-negative integer. Compute and return all derivatives up to order diff_n. Default is 0.

  Returns:
    ndarray or tuple of ndarray

      Returns a tuple of length `diff_n + 1` (if `diff_n > 0`). The first entry corresponds to the spherical harmonics, the second entry (if `diff_n >= 1`) to the gradient, and the third entry (if `diff_n >= 2`) to the Hessian matrix. Each entry is an array of shape `(n + 1, 2 * m + 1, ...)`, where the entry at `(i, j)` corresponds to degree `i` and order `j` for all `0 <= i <= n` and `-m <= j <= m`.

  See also

  `sph_harm_y`