`scipy.special._multiufuncs:sph_harm_y_all`

Signature

def sph_harm_y_all(n, m, theta, phi, *, diff_n = 0)

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

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.

: 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.