# scipy.special.roots_jacobi

scipy.special.roots_jacobi(n, alpha, beta, mu=False)

  Gauss-Jacobi quadrature.

  Compute the sample points and weights for Gauss-Jacobi quadrature. The sample points are the roots of the nth degree Jacobi polynomial, \(P^{\alpha, \beta}_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([-1, 1]\) with weight function \(w(x) = (1 - x)^{\alpha} (1 + x)^{\beta}\). See 22.2.1 in [AS] for details.

  Parameters
    n int

      quadrature order

    alpha float

      alpha must be > -1

    beta float

      beta must be > -1

    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`

  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.roots_chebys scipy.special.roots_laguerre