scipy.special.roots_legendre

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

Gauss-Legendre quadrature.

Compute the sample points and weights for Gauss-Legendre quadrature. The sample points are the roots of the nth 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 \(w(x) = 1.0\). See 2.2.10 in [AS] for more 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

See also

scipy.integrate.quadrature

scipy.integrate.fixed_quad

numpy.polynomial.legendre.leggauss

References

AS

Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.

scipy.special.eval_sh_jacobi scipy.special.roots_chebyt