def pdf_Gates_Gaudin_Schuhman_basis_integral(d, d_characteristic, m, n):
    """Calculates the integral of the multiplication of d^n by the Gates, 
    Gaudin and Schuhman (GGS) model given a particle diameter `d`,
    characteristic (maximum) particle diameter `d_characteristic`, and exponent
    `m`.
    
    .. math::
        \\int d^n\\cdot q(d)\\; dd =\\frac{m}{m+n} d^n \\left(\\frac{d}
        {d_{characteristic}}\\right)^m
        
    Parameters
    ----------
    d : float
        Specified particle diameter, [m]
    d_characteristic : float
        Characteristic particle diameter; in this model, it is the largest 
        particle size diameter in the distribution, [m]
    m : float
        Particle size distribution exponent, [-]    
    n : int
        Exponent of the multiplied n, [-]

    Returns
    -------
    pdf_basis_integral : float
        Integral of Rosin Rammler pdf multiplied by d^n, [-]

    Notes
    -----
    This integral does not have any numerical issues as `d` approaches 0.

    Examples
    --------
    >>> pdf_Gates_Gaudin_Schuhman_basis_integral(d=2E-4, d_characteristic=1E-3, m=2.3, n=-3)
    -10136984887.543015
    """
    return m / (m + n) * d ** n * (d / d_characteristic) ** m
