scipy.special.p_roots

scipy.special.p_roots(n, mu=False)

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 \(P_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) 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

See also

scipy.integrate.quadrature, scipy.integrate.fixed_quad, numpy.polynomial.legendre.leggauss