(n, a, b, x)
return jacobi(n, a, b, x) / sqrt(nfactor)
r"""
    Jacobi polynomial :math:`P_n^{\left(\alpha, \beta\right)}(x)`

    jacobi_normalized(n, alpha, beta, x) gives the nth Jacobi polynomial
    in x, :math:`P_n^{\left(\alpha, \beta\right)}(x)`.

    The Jacobi polynomials are orthogonal on :math:`[-1, 1]` with respect
    to the weight :math:`\left(1-x\right)^\alpha \left(1+x\right)^\beta`.

    This functions returns the polynomials normilzed:

    .. math::

        \int_{-1}^{1}
          P_m^{\left(\alpha, \beta\right)}(x)
          P_n^{\left(\alpha, \beta\right)}(x)
          (1-x)^{\alpha} (1+x)^{\beta} \mathrm{d}x
        = \delta_{m,n}

    Examples
    ========

    >>> from sympy import jacobi_normalized
    >>> from sympy.abc import n,a,b,x

    >>> jacobi_normalized(n, a, b, x)
    jacobi(n, a, b, x)/sqrt(2**(a + b + 1)*gamma(a + n + 1)*gamma(b + n + 1)/((a + b + 2*n + 1)*factorial(n)*gamma(a + b + n + 1)))

    See Also
    ========

    gegenbauer,
    chebyshevt_root, chebyshevu, chebyshevu_root,
    legendre, assoc_legendre,
    hermite,
    laguerre, assoc_laguerre,
    sympy.polys.orthopolys.jacobi_poly,
    sympy.polys.orthopolys.gegenbauer_poly
    sympy.polys.orthopolys.chebyshevt_poly
    sympy.polys.orthopolys.chebyshevu_poly
    sympy.polys.orthopolys.hermite_poly
    sympy.polys.orthopolys.legendre_poly
    sympy.polys.orthopolys.laguerre_poly

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Jacobi_polynomials
    .. [2] http://mathworld.wolfram.com/JacobiPolynomial.html
    .. [3] http://functions.wolfram.com/Polynomials/JacobiP/
r"""
    Jacobi polynomial :math:`P_n^{\left(\alpha, \beta\right)}(x)`
r Jacobi polynomial : math : P_n^ { \ left ( \ alpha \ beta \ right ) } ( x )
def jacobi_normalized(n, a, b, x):
    r"""
    Jacobi polynomial :math:`P_n^{\left(\alpha, \beta\right)}(x)`

    jacobi_normalized(n, alpha, beta, x) gives the nth Jacobi polynomial
    in x, :math:`P_n^{\left(\alpha, \beta\right)}(x)`.

    The Jacobi polynomials are orthogonal on :math:`[-1, 1]` with respect
    to the weight :math:`\left(1-x\right)^\alpha \left(1+x\right)^\beta`.

    This functions returns the polynomials normilzed:

    .. math::

        \int_{-1}^{1}
          P_m^{\left(\alpha, \beta\right)}(x)
          P_n^{\left(\alpha, \beta\right)}(x)
          (1-x)^{\alpha} (1+x)^{\beta} \mathrm{d}x
        = \delta_{m,n}

    Examples
    ========

    >>> from sympy import jacobi_normalized
    >>> from sympy.abc import n,a,b,x

    >>> jacobi_normalized(n, a, b, x)
    jacobi(n, a, b, x)/sqrt(2**(a + b + 1)*gamma(a + n + 1)*gamma(b + n + 1)/((a + b + 2*n + 1)*factorial(n)*gamma(a + b + n + 1)))

    See Also
    ========

    gegenbauer,
    chebyshevt_root, chebyshevu, chebyshevu_root,
    legendre, assoc_legendre,
    hermite,
    laguerre, assoc_laguerre,
    sympy.polys.orthopolys.jacobi_poly,
    sympy.polys.orthopolys.gegenbauer_poly
    sympy.polys.orthopolys.chebyshevt_poly
    sympy.polys.orthopolys.chebyshevu_poly
    sympy.polys.orthopolys.hermite_poly
    sympy.polys.orthopolys.legendre_poly
    sympy.polys.orthopolys.laguerre_poly

    References
    ==========

    .. [1] http://en.wikipedia.org/wiki/Jacobi_polynomials
    .. [2] http://mathworld.wolfram.com/JacobiPolynomial.html
    .. [3] http://functions.wolfram.com/Polynomials/JacobiP/
    """
    nfactor = (S(2)**(a + b + 1) * (gamma(n + a + 1) * gamma(n + b + 1))
               / (2*n + a + b + 1) / (factorial(n) * gamma(n + a + b + 1)))

    return jacobi(n, a, b, x) / sqrt(nfactor)
def jacobi_normalized ( n , a , b , x ) : nfactor = ( S ( 2 ) ** ( a + b + 1 ) * ( gamma ( n + a + 1 ) * gamma ( n + b + 1 ) ) / ( 2 * n + a + b + 1 ) / ( factorial ( n ) * gamma ( n + a + b + 1 ) ) ) return jacobi ( n , a , b , x ) / sqrt ( nfactor )