parameters: (n, k, maxit=5)
return_statement: return xi
docstring: 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
docstring_summary: Helper function for Tricomi initial guesses
docstring_tokens: Helper function for Tricomi initial guesses
function: 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
function_tokens: def _compute_tauk ( n , k , maxit = 5 ) : 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