def _h13_s(s):
    """Define the boundary between Region 1 and 3, h=f(s)

    Parameters
    ----------
    s : float
        Specific entropy, [kJ/kgK]

    Returns
    -------
    h : float
        Specific enthalpy, [kJ/kg]

    Notes
    ------
    Raise :class:`NotImplementedError` if input isn't in limit:

        * s(100MPa,623.15K) ≤ s ≤ s'(623.15K)

    References
    ----------
    IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
    Region 3, Equations as a Function of h and s for the Region Boundaries, and
    an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
    for the Thermodynamic Properties of Water and Steam,
    http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 7

    Examples
    --------
    >>> _h13_s(3.7)
    1632.525047
    >>> _h13_s(3.5)
    1566.104611
    """
    if s < 3.397782955 or s > 3.77828134:
        raise NotImplementedError('Incoming out of bound')
    sigma = s / 3.8
    I = [0, 1, 1, 3, 5, 6]
    J = [0, -2, 2, -12, -4, -3]
    n = [0.913965547600543, -4.30944856041991e-05, 60.3235694765419, 
        1.17518273082168e-18, 0.220000904781292, -69.0815545851641]
    suma = 0
    for i, j, ni in zip(I, J, n):
        suma += ni * (sigma - 0.884) ** i * (sigma - 0.864) ** j
    return 1700 * suma
