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Research Article Open access CC BY 4.0

Monotonicity and Convexity Properties and Some Inequalities Involving a Generalized Form of the Wallis' Cosine Formula

Kwara Nantomah

Asian Research Journal of Mathematics · pp. 1–10 · Published 25 Sep 2017

10.9734/ARJOM/2017/36699

Abstract

This study is focused on monotonicity and convexity properties of a generalized form of the Wallis’ cosine formula. Specifically, by using the integral form of the Nielsen’s β-function, we prove that the generalized Wallis’ cosine formula is logarithmically completely monotonic, logarithmically convex and decreasing. Furthermore, by using the classical Wendel’s, Hölder’s and Young’s inequalities, among other analytical techniques, we establish some new inequalities involving the generalized function.

Nielsen's β-function Wendel's inequality Hölder's inequality Young's inequality logarithmically completely monotonic function Wallis' cosine formula.

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Cited by 8

Some monotonicity properties and inequalities for the generalized digamma and polygamma functions

Li Yin, Li-Guo Huang, Zhi-Min Song · Journal of Inequalities and Applications · 2018

New Inequalities for Nielsen’s Beta Function

Kwara Nantomah · Communications in Mathematics and Applications · 2019

Some analytical properties of the Nielsen's beta function

Kwara Nantomah · Gulf Journal of Mathematics · 2025

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