Using series expansion, the Z-scan characteristics of thin optically nonlinear medium are analyzed. Through discussing series expansion and Fresnel intergral method, It is verified that Gaussian decomposition method is equivalent to Fresnel integral method for(Z-scan) measurements of a thin medium using a Gaussian light beam even for a large nonlinear phase shift, and clarify some misunderstandings. Meanwhile, the relationship of normalized transmittance with upper limiter of Fresnel integral is analyzed, the reason for the oscillation of series summation is given and a criterion for minimum summation number of series needed to eliminate the oscillation is suggested while using a Gaussian decomposition method. The situations that are suitable to be applied for Gaussian decomposition method and Fresnel intergral method are discussed. The conclusion given can be used to choose the appropriate and high efficient analytic method in experimental and theoretical analysis.