Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-03-01

Journal: RESULTS IN MATHEMATICS

Included Journals: SCIE

Volume: 73

Issue: 1

ISSN: 1422-6383

Key Words: Mills' ratio; asymptotic series; fraction approximation; double inequality

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.