Abstract
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.
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