A curious relation between the flat cosmological model and the elliptic
  integral of the first kind
  The dependence of the luminosity distance on the redshift has a key
importance in the cosmology. This dependence can well be given by standard
functions for the zero cosmological constant. The purpose of this article is to
present such a relation also for the non-zero cosmological constant, if the
universe is spatially flat. A definite integral is used. The integration ends
in the elliptic integral of the first kind. The result shows that no numerical
integration is needed for the non-zero cosmological constant, if the universe
is spatially flat.
