# scipy.special.legendre

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

  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:
    n int

      Degree of the polynomial.

    monic bool, optional

      If True, scale the leading coefficient to be 1. Default is False.

  Returns:
    P orthopoly1d

      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. ])