The concept of moments, which are integrals of positive or negative integral powers ωn weighted by real or imaginary parts of admittance functions, is here generalized so as to be applied to a wide category of admittance functions, including Lorentzian functions. The generalized moments are related to the derivatives or integrals of sum rules in a general sense. This analysis is based on differentiation and integration-mapping of admittance functions and the associated Kramers-Kronig relations. Some model calculations are also shown.