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论文类型：期刊论文

发表时间：2018-03-01

发表刊物：RESULTS IN MATHEMATICS

收录刊物：SCIE

卷号：73

期号：1

ISSN号：1422-6383

关键字：Mills' ratio; asymptotic series; fraction approximation; double inequality

摘要：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.