Results in Mathematics

, 73:27 | Cite as

Some New Approximations and Proofs for Mills’ Ratio



In this paper, we present some new proofs for asymptotic series of Mills’ ratio. Given these new inequalities, the upper bound of the error of Mills’ ratio can be estimated more exactly. Next, a new double inequality related to this asymptotic series is established. For demonstrating the superiority of our new inequality over the original formula and other classical or recently discovered asymptotic series, some numerical computations are provided. Finally, we give a table of Mills’ ratio.


Mills’ ratio asymptotic series fraction approximation double inequality 

Mathematics Subject Classification

26A48 26D10 33B20 41A17 62E17 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianChina
  2. 2.Graduate School of Arts and SciencesColumbia UniversityNew YorkUnited States

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