scipy.special.legendre

scipy.special.legendre(n, monic=False)

Legendre polynomial coefficients

Returns the nth-order Legendre polynomial, P_n(x), orthogonal over [-1, 1] with weight function 1.

Parameters:

n

Order of the polynomial

monic : bool, optional

If True, output is a monic polynomial (normalized so the leading coefficient is 1). Default is False.

Returns:

P : orthopoly1d

The Legendre polynomial object

Examples

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

>>> legendre(3)
poly1d([ 2.5,  0. , -1.5, -0. ])