New Inequalities of Cusa–Huygens Type

Open AccessArticle

by

Ling Zhu

Department of Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Mathematics 2021, 9(17), 2101; https://doi.org/10.3390/math9172101

Submission received: 16 July 2021 / Revised: 26 August 2021 / Accepted: 27 August 2021 / Published: 31 August 2021

(This article belongs to the Section E1: Mathematics and Computer Science)

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Abstract

Using the power series expansions of the functions

cot x, 1 / sin x

and

1 / {sin}^{2} x

, and the estimate of the ratio of two adjacent even-indexed Bernoulli numbers, we improve Cusa–Huygens inequality in two directions on

(0, π / 2)

. Our results are much better than those in the existing literature.

Keywords: sharp the double inequalities of Cusa–Huygens type; circular functions; Bernoulli numbers

MDPI and ACS Style

Zhu, L. New Inequalities of Cusa–Huygens Type. Mathematics 2021, 9, 2101. https://doi.org/10.3390/math9172101

AMA Style

Zhu L. New Inequalities of Cusa–Huygens Type. Mathematics. 2021; 9(17):2101. https://doi.org/10.3390/math9172101

Chicago/Turabian Style

Zhu, Ling. 2021. "New Inequalities of Cusa–Huygens Type" Mathematics 9, no. 17: 2101. https://doi.org/10.3390/math9172101

APA Style

Zhu, L. (2021). New Inequalities of Cusa–Huygens Type. Mathematics, 9(17), 2101. https://doi.org/10.3390/math9172101

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