  Recently we have found an analytic integration formula that describes the
dependence of the luminosity distance on the redshift for the flat cosmological
model with a non-zero cosmological constant. The purpose of this article is to
search for a similar relation for the non-flat models. A Taylor series was
used. The elliptic integral of the first kind can indeed be applied. The result
shows that a combination of the numerical integration with the previous
analytic formula can also be useful for the nearly flat cosmological models.
