平坦宇宙模型与第一类椭圆积分之间的一个奇妙关系
A curious relation between the flat cosmological model and the elliptic integral of the first kind
摘要：
光度距离对红移的依赖性在宇宙学中具有关键的重要性。这种依赖关系可以用宇宙学常数为零的标准函数来给出。本文的目的是提出这样的关系也为非零的宇宙学常数，如果宇宙是空间平坦的。使用定积分。积分以第一类椭圆积分结束。结果表明，如果宇宙是空间平坦的，则对非零的宇宙学常数不需要数值积分。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
