def j0_4(f=1, rho=0.3, z=50):
    r"""Hankel transform pair J0_4 ([ChCo82]_).

    Parameters
    ----------
    f : float
        Frequency (Hz)
    rho : float
        Resistivity (Ohm.m)
    z : float
        Vertical distance between source and receiver (m)

    """

    gam = np.sqrt(2j*np.pi*mu_0*f/rho)

    def lhs(x):
        beta = np.sqrt(x**2 + gam**2)
        return x*np.exp(-beta*np.abs(z))/beta

    def rhs(b):
        R = np.sqrt(b**2 + z**2)
        return np.exp(-gam*R)/R

    return Ghosh('j0', lhs, rhs)