SciPy

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 \(P_n(x)\). 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
nint

quadrature order

mubool, optional

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

Returns
xndarray

Sample points

wndarray

Weights

mufloat

Sum of the weights

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