`scipy.special._orthogonal:_initial_nodes_a`

source: /scipy/special/_orthogonal.py :949

Signature

def _initial_nodes_a ( n , k )

Summary

Tricomi initial guesses

Extended Summary

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 $2 n + 1$ .

Parameters

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

Returns

xksq : ndarray: Square of the approximate roots

Aliases