code: def _compute_tauk(n, k, maxit=5):
      """Helper function for Tricomi initial guesses
  
      For details, see formula 3.1 in lemma 3.1 in the
      original paper.
  
      Parameters
      ----------
      n : int
          Quadrature order
      k : ndarray of type int
          Index of roots :math:`\tau_k` to compute
      maxit : int
          Number of Newton maxit performed, the default
          value of 5 is sufficient.
  
      Returns
      -------
      tauk : ndarray
          Roots of equation 3.1
  
      See Also
      --------
      initial_nodes_a
      roots_hermite_asy
      """
      a = n % 2 - 0.5
      c = (
          (4.0 * floor(n / 2.0) - 4.0 * k + 3.0)
          * pi
          / (4.0 * floor(n / 2.0) + 2.0 * a + 2.0)
      )
      f = lambda x: x - sin(x) - c
      df = lambda x: 1.0 - cos(x)
      xi = 0.5 * pi
      for i in range(maxit):
          xi = xi - f(xi) / df(xi)
      return xi
  
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 11 for calling a global function with example usage: _compute_tauk(n, k, maxit) and returns: xi