  The slow-roll approximation is an analytical approach to study dynamical
properties of the inflationary universe. In this article, systematic
construction of the slow-roll expansion for effective loop quantum cosmology is
presented. The analysis is performed up to the fourth order in both slow-roll
parameters and the parameter controlling the strength of deviation from the
classical case. The expansion is performed for three types of the slow-roll
parameters: Hubble slow-roll parameters, Hubble flow parameters and potential
slow-roll parameters. An accuracy of the approximation is verified by
comparison with the numerical phase space trajectories for the case with a
massive potential term. The results obtained in this article may be helpful in
the search for the subtle quantum gravitational effects with use of the
cosmological data.
