scipy.special.

roots_sh_jacobi

scipy.special.roots_sh_jacobi(n, p1, q1, mu=False)

Gauss-Jacobi (shifted) quadrature.

Compute the sample points and weights for Gauss-Jacobi (shifted) quadrature. The sample points are the roots of the nth degree shifted Jacobi polynomial, \(G^{p,q}_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([0, 1]\) with weight function \(w(x) = (1 - x)^{p-q} x^{q-1}\). See 22.2.2 in [AS] for details.

Parameters:

nint

quadrature order

p1float

(p1 - q1) must be > -1

q1float

q1 must be > 0

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

References

[AS]

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