`numpy.polynomial.laguerre:laggauss`

source: /numpy/polynomial/laguerre.py :1531

Signature

def laggauss ( deg )

Summary

Gauss-Laguerre quadrature.

Extended Summary

Computes the sample points and weights for Gauss-Laguerre quadrature. These sample points and weights will correctly integrate polynomials of degree $2 * d e g - 1$ or less over the interval $[0, in f]$ with the weight function $f (x) = exp (- x)$ .

Parameters

deg : int: Number of sample points and weights. It must be >= 1.

Returns

x : ndarray: 1-D ndarray containing the sample points.
y : ndarray: 1-D ndarray containing the weights.

Notes

The results have only been tested up to degree 100 higher degrees may be problematic. The weights are determined by using the fact that

w_{k} = c / (L_{n}^{'} (x_{k}) * L_{n - 1} (x_{k}))

where $c$ is a constant independent of $k$ and $x_{k}$ is the k'th root of $L_{n}$ , and then scaling the results to get the right value when integrating 1.

Examples

from numpy.polynomial.laguerre import laggauss

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laggauss(2)

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Aliases

numpy.polynomial.laguerre.laggauss