numpy.polynomial.hermite_e.hermegauss¶
- numpy.polynomial.hermite_e.hermegauss(deg)[source]¶
Gauss-HermiteE quadrature.
Computes the sample points and weights for Gauss-HermiteE quadrature. These sample points and weights will correctly integrate polynomials of degree 2*deg - 1 or less over the interval [-\inf, \inf] with the weight function f(x) = \exp(-x^2/2).
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 / (He'_n(x_k) * He_{n-1}(x_k))
where c is a constant independent of k and x_k is the k’th root of He_n, and then scaling the results to get the right value when integrating 1.