scipy.special.

roots_sh_legendre#

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

Gauss-Legendre (shifted) quadrature.

Compute the sample points and weights for Gauss-Legendre quadrature. The sample points are the roots of the nth degree shifted Legendre polynomial \(P^*_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([0, 1]\) with weight function \(w(x) = 1.0\). See 2.2.11 in [AS] for details.

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