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Indexed by:期刊论文

First Author:Fang, Siyu

Correspondence Author:Fang, SY (reprint author), Dalian Univ Technol, Sch Math Sci, Dalian 116023, Peoples R China.

Co-author:Lai, Li,Lu, Dawei,Wang, Xiaoguang

Date of Publication:2018-06-01

Journal:RESULTS IN MATHEMATICS

Included Journals:SCIE

Volume:73

Issue:2

ISSN No.: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.