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Liu, D.-Z., Ma, C., Zhang, T.-J. and Yang, Z. (2011) Numerical Strategies of Computing the Luminosity Distance. Monthly Notices of the Royal Astronomical Society, 412, 2685-2688.
https://doi.org/10.1111/j.1365-2966.2010.18101.x

has been cited by the following article:

• TITLE: Legendre-Jacobi’s Elliptic Integrals Shed Light on the Luminosity Distance in Cosmology

  AUTHORS: Alessandro Trinchera

  KEYWORDS: Cosmology, Distance Luminosity, Transverse Comoving Distance, Incomplete Elliptic Integrals

  JOURNAL NAME: Journal of High Energy Physics, Gravitation and Cosmology, Vol.10 No.3, July 3, 2024

  ABSTRACT: This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.