(n, n_digits)
return xi, w
r"""
    Computes the Gauss-Chebyshev quadrature [1]_ points and weights of
    the second kind.

    The Gauss-Chebyshev quadrature of the second kind approximates the integral:

    .. math::
        \int_{-1}^{1} \sqrt{1-x^2} f(x)\,dx \approx \sum_{i=1}^n w_i f(x_i)

    The nodes `x_i` of an order `n` quadrature rule are the roots of `U_n`
    and the weights `w_i` are given by:

    .. math::
        w_i = \frac{\pi}{n+1} \sin^2 \left(\frac{i}{n+1}\pi\right)

    Parameters
    ==========

    n : the order of quadrature

    n_digits : number of significant digits of the points and weights to return

    Returns
    =======

    (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats.
             The points `x_i` and weights `w_i` are returned as ``(x, w)``
             tuple of lists.

    Examples
    ========

    >>> from sympy import S
    >>> from sympy.integrals.quadrature import gauss_chebyshev_u
    >>> x, w = gauss_chebyshev_u(3, 5)
    >>> x
    [0.70711, 0, -0.70711]
    >>> w
    [0.3927, 0.7854, 0.3927]

    >>> x, w = gauss_chebyshev_u(6, 5)
    >>> x
    [0.90097, 0.62349, 0.22252, -0.22252, -0.62349, -0.90097]
    >>> w
    [0.084489, 0.27433, 0.42658, 0.42658, 0.27433, 0.084489]

    See Also
    ========

    gauss_legendre, gauss_laguerre, gauss_hermite, gauss_gen_laguerre, gauss_chebyshev_t, gauss_jacobi

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Chebyshev%E2%80%93Gauss_quadrature
    .. [2] http://people.sc.fsu.edu/~jburkardt/cpp_src/chebyshev2_rule/chebyshev2_rule.html
r"""
    Computes the Gauss-Chebyshev quadrature [1]_ points and weights of
    the second kind.
r Computes the Gauss - Chebyshev quadrature [ 1 ] _ points and weights of the second kind .
def gauss_chebyshev_u(n, n_digits):
    r"""
    Computes the Gauss-Chebyshev quadrature [1]_ points and weights of
    the second kind.

    The Gauss-Chebyshev quadrature of the second kind approximates the integral:

    .. math::
        \int_{-1}^{1} \sqrt{1-x^2} f(x)\,dx \approx \sum_{i=1}^n w_i f(x_i)

    The nodes `x_i` of an order `n` quadrature rule are the roots of `U_n`
    and the weights `w_i` are given by:

    .. math::
        w_i = \frac{\pi}{n+1} \sin^2 \left(\frac{i}{n+1}\pi\right)

    Parameters
    ==========

    n : the order of quadrature

    n_digits : number of significant digits of the points and weights to return

    Returns
    =======

    (x, w) : the ``x`` and ``w`` are lists of points and weights as Floats.
             The points `x_i` and weights `w_i` are returned as ``(x, w)``
             tuple of lists.

    Examples
    ========

    >>> from sympy import S
    >>> from sympy.integrals.quadrature import gauss_chebyshev_u
    >>> x, w = gauss_chebyshev_u(3, 5)
    >>> x
    [0.70711, 0, -0.70711]
    >>> w
    [0.3927, 0.7854, 0.3927]

    >>> x, w = gauss_chebyshev_u(6, 5)
    >>> x
    [0.90097, 0.62349, 0.22252, -0.22252, -0.62349, -0.90097]
    >>> w
    [0.084489, 0.27433, 0.42658, 0.42658, 0.27433, 0.084489]

    See Also
    ========

    gauss_legendre, gauss_laguerre, gauss_hermite, gauss_gen_laguerre, gauss_chebyshev_t, gauss_jacobi

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Chebyshev%E2%80%93Gauss_quadrature
    .. [2] http://people.sc.fsu.edu/~jburkardt/cpp_src/chebyshev2_rule/chebyshev2_rule.html
    """
    x = Dummy("x")
    xi = []
    w  = []
    for i in xrange(1,n+1):
        xi.append((cos(i/(n+S.One)*S.Pi)).n(n_digits))
        w.append((S.Pi/(n+S.One)*sin(i*S.Pi/(n+S.One))**2).n(n_digits))
    return xi, w
def gauss_chebyshev_u ( n , n_digits ) : x = Dummy ( "x" ) xi = [ ] w = [ ] for i in xrange ( 1 , n + 1 ) : xi . append ( ( cos ( i / ( n + S . One ) * S . Pi ) ) . n ( n_digits ) ) w . append ( ( S . Pi / ( n + S . One ) * sin ( i * S . Pi / ( n + S . One ) ) ** 2 ) . n ( n_digits ) ) return xi , w