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Recently we have found an analytic integration formula that describes thedependence of the luminosity distance on the redshift for the flat cosmologicalmodel with a non-zero cosmological constant. The purpose of this article is tosearch for a similar relation for the non-flat models. A Taylor series wasused. The elliptic integral of the first kind can indeed be applied. The resultshows that a combination of the numerical integration with the previousanalytic formula can also be useful for the nearly flat cosmological models.

On the relation between the non-flat cosmological models and the elliptic integral of first kind