`scipy.special._orthogonal:_initial_nodes_b`

source: /scipy/special/_orthogonal.py :984

Signature

def _initial_nodes_b ( n , k )

Summary

Gatteschi initial guesses

Extended Summary

Computes an initial approximation to the square of the kth (positive) root $x_{k}$ of the Hermite polynomial $H_{n}$ of order $n$ . The formula is the one from lemma 3.2 in the original paper. The guesses are accurate in the region just below $2 n + 1$ .

Parameters

n : int: Quadrature order
k : ndarray of type int: Index of roots to compute

Returns

xksq : ndarray: Square of the approximate root

Aliases