scipy.special.roots_legendre¶
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scipy.special.
roots_legendre
(n, mu=False)[source]¶ 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
References
- AS
Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.