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hermegauss(deg)

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 $f(x) = \exp(-x^2/2)$ .

Notes

versionadded

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.

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.

Gauss-HermiteE quadrature.

Examples

See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /numpy/polynomial/hermite_e.py#1552
type: <class 'function'>
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