def log_series_diff(b, a):
    """ The Taylor series for log(1+b) - log(1+a).

    Parameters
    ----------
    a : ndarray
        Input for log(1+a).
    b : ndarray
        Input for log(1+b).

    Returns
    -------
    ndarray
        The Taylor series log(1+b) - log(1+a), up to the 11th order term.

    """
    return(
        - (b-a) - (b**2 - a**2)/2 - (b**3 - a**3)/3
        - (b**4 - a**4)/4 - (b**5 - a**5)/5 - (b**6 - a**6)/6
        - (b**7 - a**7)/7 - (b**8 - a**8)/8 - (b**9 - a**9)/9
        - (b**10 - a**10)/10 - (b**11 - a**11)/11
    )