`scipy.special._multiufuncs:legendre_p`

Signature

def legendre_p(n, z, *, diff_n = 0)

Legendre polynomial of the first kind.

n : array_like of ints: Degree of the Legendre polynomial. Must have n >= 0.
z : array_like: Input value.
diff_n : int, optional: A non-negative integer. Compute and return all derivatives up to order diff_n. Default is 0.

p : ndarray or tuple of ndarray: Legendre polynomial with diff_n derivatives.

Evaluate the Legendre polynomial :math:`P_3` at :math:`z = 0.5`:

import numpy as np
from scipy.special import legendre_p
np.allclose(legendre_p(3, 0.5), -0.4375)

✓

True

Compute the value and first derivative with respect to ``z``:

p, dp = legendre_p(3, 0.5, diff_n=1)
np.allclose([p, dp], [-0.4375, 0.375])

✓

True