code: def roots_gegenbauer(n, alpha, mu=False):
      r"""Gauss-Gegenbauer quadrature.
  
      Computes the sample points and weights for Gauss-Gegenbauer quadrature.
      The sample points are the roots of the n-th degree Gegenbauer polynomial,
      :math:`C^{\alpha}_n(x)`.  These sample points and weights correctly
      integrate polynomials of degree :math:`2n - 1` or less over the interval
      :math:`[-1, 1]` with weight function
      :math:`f(x) = (1 - x^2)^{\alpha - 1/2}`.
  
      Parameters
      ----------
      n : int
          quadrature order
      alpha : float
          alpha must be > -0.5
      mu : bool, optional
          If True, return the sum of the weights, optional.
  
      Returns
      -------
      x : ndarray
          Sample points
      w : ndarray
          Weights
      mu : float
          Sum of the weights
  
      See Also
      --------
      scipy.integrate.quadrature
      scipy.integrate.fixed_quad
      """
      m = int(n)
      if n < 1 or n != m:
          raise ValueError("n must be a positive integer.")
      if alpha < -0.5:
          raise ValueError("alpha must be greater than -0.5.")
      elif alpha == 0.0:
          # C(n,0,x) == 0 uniformly, however, as alpha->0, C(n,alpha,x)->T(n,x)
          # strictly, we should just error out here, since the roots are not
          # really defined, but we used to return something useful, so let's
          # keep doing so.
          return roots_chebyt(n, mu)
  
      mu0 = (
          np.sqrt(np.pi)
          * cephes.gamma(alpha + 0.5)
          / cephes.gamma(alpha + 1)
      )
      an_func = lambda k: 0.0 * k
      bn_func = lambda k: np.sqrt(
          k * (k + 2 * alpha - 1) / (4 * (k + alpha) * (k + alpha - 1))
      )
      f = lambda n, x: cephes.eval_gegenbauer(n, alpha, x)
      df = lambda n, x: (
          -n * x * cephes.eval_gegenbauer(n, alpha, x)
          + (n + 2 * alpha - 1)
          * cephes.eval_gegenbauer(n - 1, alpha, x)
      ) / (1 - x**2)
      return _gen_roots_and_weights(
          m, mu0, an_func, bn_func, f, df, True, mu
      )
  
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 21 for calling a global function with example usage: roots_gegenbauer(n, alpha, mu) and returns: _gen_roots_and_weights, roots_chebyt