roots_jacobi — SciPy v1.15.2 Manual (original) (raw)

scipy.special.

scipy.special.roots_jacobi(n, alpha, beta, mu=False)[source]#

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:

nint

quadrature order

alphafloat

alpha must be > -1

betafloat

beta must be > -1

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.