The framework of the theoretical treatment for finite energy sum rule is generalized to deal with both the ground state and the excited resonances of baryons in the same way

namely

all the spectrum functions of the ground and considered excited baryon states appearing in the dispersion relations are described by similar Breit-Wigner resonance form of finite width

and derivation of the masses and widths of the considered three low-lying resonances is also on the same footing.We expand Singh’s method and work out the complete set of the equations for the finite-energy sum rules

including both expressions in the theoretical and the phenomenological sides.Based on these works

the numerical simulation methods are used to obtain the final results which are reasonably in agreement with the experimental data within the typical error of sum rule method.