scipy.special.legendre¶
-
scipy.special.legendre(n, monic=False)[source]¶ Legendre polynomial.
Defined to be the solution of
\[\frac{d}{dx}\left[(1 - x^2)\frac{d}{dx}P_n(x)\right] + n(n + 1)P_n(x) = 0;\]\(P_n(x)\) is a polynomial of degree \(n\).
- Parameters
- nint
Degree of the polynomial.
- monicbool, optional
If True, scale the leading coefficient to be 1. Default is False.
- Returns
- Porthopoly1d
Legendre polynomial.
Notes
The polynomials \(P_n\) are orthogonal over \([-1, 1]\) with weight function 1.
Examples
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. ])