R(n) ratio boundary for selecting between [b_hi-1, b_hi]
    alpha = b + 2

def rn_boundary(af, b_hi):
    """
    R(n) ratio boundary for selecting between [b_hi-1, b_hi]
    alpha = b + 2
    
    """
    return np.sqrt( rn_theory(af, b)*rn_theory(af, b-1) )