`scipy.special._orthogonal:legendre`

Signature

def legendre(n, monic = False)

Legendre polynomial.

Defined to be the solution of

\frac{d}{d x} [(1 - x^{2}) \frac{d}{d x} P_{n} (x)] + n (n + 1) P_{n} (x) = 0;

$P_{n} (x)$ is a polynomial of degree $n$ .

n : int: Degree of the polynomial.
monic : bool, optional: If True, scale the leading coefficient to be 1. Default is False.

The polynomials $P_{n}$ are orthogonal over $[- 1, 1]$ with weight function 1.

Generate the 3rd-order Legendre polynomial 1/2*(5x^3 + 0x^2 - 3x + 0):

from scipy.special import legendre
legendre(3)

✓

poly1d([ 2.5,  0. , -1.5,  0. ])