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. ])