Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-06-01

Journal: RESULTS IN MATHEMATICS

Included Journals: SCIE

Volume: 73

Issue: 2

ISSN: 1422-6383

Key Words: Continued fraction; asymptotic formula; constant e; double inequalities; Keller's limit

Abstract: A new asymptotic formula for the constant e is proposed by the continued fraction approximation. As a consequence, we deduce inequalities for the sequence (1 + 1/n)(n), and show an application of the inequalities to the proof of Keller's limit. Numerical computations and comparisons are conducted to illustrate the superiority of our new inequalities.