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Some New Approximations and Proofs for Mills’ Ratio

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116023, China

    Dawei Lu & Lixin Song

  2. Graduate School of Arts and Sciences, Columbia University, New York, NY, 07029, United States

    Guangqing Tang

Authors
  1. Dawei Lu
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  2. Lixin Song
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  3. Guangqing Tang
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Correspondence to Lixin Song.

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Lu, D., Song, L. & Tang, G. Some New Approximations and Proofs for Mills’ Ratio. Results Math 73, 27 (2018). https://doi.org/10.1007/s00025-018-0798-5

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  • DOI: https://doi.org/10.1007/s00025-018-0798-5

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