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scipy.special.roots_legendre

scipy.special.roots_legendre(n, mu=False)[source]

Gauss-Legendre quadrature.

Computes the sample points and weights for Gauss-Legendre quadrature. The sample points are the roots of the n-th degree Legendre polynomial Pn(x). These sample points and weights correctly integrate polynomials of degree 2n1 or less over the interval [1,1] with weight function f(x)=1.0.

Parameters:

n : int

quadrature order

mu : bool, optional

If True, return the sum of the weights, optional.

Returns:

x : ndarray

Sample points

w : ndarray

Weights

mu : float

Sum of the weights