code: def _initial_nodes_b(n, k):
      r"""Gatteschi initial guesses
  
      Computes an initial approximation to the square of the `k`-th
      (positive) root :math:`x_k` of the Hermite polynomial :math:`H_n`
      of order :math:`n`. The formula is the one from lemma 3.2 in the
      original paper. The guesses are accurate in the region just
      below :math:`\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 root
  
      See Also
      --------
      initial_nodes
      roots_hermite_asy
      """
      a = n % 2 - 0.5
      nu = 4.0 * floor(n / 2.0) + 2.0 * a + 2.0
      # Airy roots by approximation
      ak = specfun.airyzo(k.max(), 1)[0][::-1]
      # Initial approximation of Hermite roots (square)
      xksq = (
          nu
          + 2.0 ** (2.0 / 3.0) * ak * nu ** (1.0 / 3.0)
          + 1.0
          / 5.0
          * 2.0 ** (4.0 / 3.0)
          * ak**2
          * nu ** (-1.0 / 3.0)
          + (9.0 / 140.0 - 12.0 / 175.0 * ak**3) * nu ** (-1.0)
          + (16.0 / 1575.0 * ak + 92.0 / 7875.0 * ak**4)
          * 2.0 ** (2.0 / 3.0)
          * nu ** (-5.0 / 3.0)
          - (
              15152.0 / 3031875.0 * ak**5
              + 1088.0 / 121275.0 * ak**2
          )
          * 2.0 ** (1.0 / 3.0)
          * nu ** (-7.0 / 3.0)
      )
      return xksq
  
imports: from __future__ import division, print_function, absolute_import
  import numpy
  from numpy import exp, inf, pi, sqrt, floor, sin, cos, around, int, hstack, arccos, arange
  from scipy import linalg
  from scipy.special import airy
  from .None import _ufuncs
  from .None import _ufuncs
  from .None import specfun
  from ._ufuncs import binom, eval_jacobi, eval_sh_jacobi, eval_gegenbauer, eval_chebyt, eval_chebyu, eval_chebys, eval_chebyc, eval_sh_chebyt, eval_sh_chebyu, eval_legendre, eval_sh_legendre, eval_genlaguerre, eval_laguerre, eval_hermite, eval_hermitenorm
label_desc: Use image node_id 13 for calling a global function with example usage: _initial_nodes_b(n, k) and returns: xksq