scipy.special.roots_laguerre

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

Gauss-Laguerre quadrature.

Compute the sample points and weights for Gauss-Laguerre quadrature. The sample points are the roots of the nth degree Laguerre polynomial, \(L_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([0, \infty]\) with weight function \(w(x) = e^{-x}\). See 22.2.13 in [AS] for 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.laguerre.laggauss

References

[AS]

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