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Some new approximations and inequalities of the sequence (1+1/n)(n) and improvements of Carleman's inequality

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Indexed by:期刊论文

Date of Publication:2017-05-01

Journal:RAMANUJAN JOURNAL

Included Journals:SCIE

Volume:43

Issue:1

Page Number:69-82

ISSN No.: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.

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