This paper introduces key properties that are useful for the computation of a Taylor expansion of discretization zeros or single intrinsic zeros of sampled-data systems. Furthermore, regularity is shown to exist in the suffixes of the coefficients of the expansion expressions, which implies that the sampling zeros or every coefficient in the numerator of the transfer function of the sampled-data systems is dominated by the coefficients of higher order terms in the numerator and denominator of the continuous-time counterpart. Moreover, it is shown that the regularity can reduce the calculation effort for expansions of higher order systems.