parameters: (n, p1, q1, mu=False)
docstring: Gauss-Jacobi (shifted) quadrature.
  
      Computes the sample points and weights for Gauss-Jacobi (shifted)
      quadrature. The sample points are the roots of the n-th degree shifted
      Jacobi polynomial, :math:`G^{p,q}_n(x)`.  These sample points and weights
      correctly integrate polynomials of degree :math:`2n - 1` or less over the
      interval :math:`[0, 1]` with weight function
      :math:`f(x) = (1 - x)^{p-q} x^{q-1}`
  
      Parameters
      ----------
      n : int
          quadrature order
      p1 : float
          (p1 - q1) must be > -1
      q1 : float
          q1 must be > 0
      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
docstring_summary: Gauss-Jacobi (shifted) quadrature.
docstring_tokens: Gauss - Jacobi ( shifted ) quadrature .
function: def roots_sh_jacobi(n, p1, q1, mu=False):
      """Gauss-Jacobi (shifted) quadrature.
  
      Computes the sample points and weights for Gauss-Jacobi (shifted)
      quadrature. The sample points are the roots of the n-th degree shifted
      Jacobi polynomial, :math:`G^{p,q}_n(x)`.  These sample points and weights
      correctly integrate polynomials of degree :math:`2n - 1` or less over the
      interval :math:`[0, 1]` with weight function
      :math:`f(x) = (1 - x)^{p-q} x^{q-1}`
  
      Parameters
      ----------
      n : int
          quadrature order
      p1 : float
          (p1 - q1) must be > -1
      q1 : float
          q1 must be > 0
      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
      """
      if (p1-q1) <= -1 or q1 <= 0:
          raise ValueError("(p - q) must be greater than -1, and q must be greater than 0.")
      x, w, m = roots_jacobi(n, p1-q1, q1-1, True)
      x = (x + 1) / 2
      scale = 2.0**p1
      w /= scale
      m /= scale
      if mu:
          return x, w, m
      else:
          return x, w
function_tokens: def roots_sh_jacobi ( n , p1 , q1 , mu = False ) : if ( p1 - q1 ) <= - 1 or q1 <= 0 : raise ValueError ( "(p - q) must be greater than -1, and q must be greater than 0." ) x , w , m = roots_jacobi ( n , p1 - q1 , q1 - 1 , True ) x = ( x + 1 ) / 2 scale = 2.0 ** p1 w /= scale m /= scale if mu : return x , w , m else : return x , w