def capital_pi1(x, w):
    """
    Calculates PI_1 value for fqe_I
    Related to the self energy of the dynamic susceptibility

    Parameters
    ----------
    x               :   float
        q (momentum transfer) / kappa (inverse mag. correlation length)
    w               :   float

    Return
    ------
    PI_1            :   float
    """
    a = 0.46
    b = 3.16
    return ((1 + b/x**2)**(2 - 3.0/4) - 1j * a * w)**(3.0/5)