Some new approximations and inequalities of the sequence (1+1/n)(n) and improvements of Carleman's inequality
Release Time:2019-03-12 Hits:
Indexed by: Journal Article
Date of Publication: 2017-05-01
Journal: RAMANUJAN JOURNAL
Included Journals: SCIE
Volume: 43
Issue: 1
Page Number: 69-82
ISSN: 1382-4090
Key Words: Polynomial approximation; Continued fraction; Constant e; Carleman's inequality; Double inequalities
Abstract: In this paper, using the polynomial approximation and the continued fraction approximation, we present some sharp inequalities for the sequence and some applications to Carleman's inequality. For demonstrating the superiority of our new inequalities over the classical one, some proofs and numerical computations are provided.