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_initial_nodes_a(n, k)

Computes an initial approximation to the square of the k-th (positive) root $x_k$ of the Hermite polynomial $H_n$ of order $n$ . The formula is the one from lemma 3.1 in the original paper. The guesses are accurate except in the region near $\sqrt{2n + 1}$ .

Parameters

n : int

Quadrature order

k : ndarray of type int

Index of roots to compute

Returns

xksq : ndarray

Square of the approximate roots

Tricomi initial guesses

See Also

initial_nodes
roots_hermite_asy

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 : /scipy/special/_orthogonal.py#917
type: <class 'function'>
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