Table of Content
trigonometric functions
Open AccessArticleOn Some Trigonometric and Inverse Trigonometric Integral Formulas
Christophe Chesneau
Annals of Communications in Mathematics 2025,
8 (3),
386-392
DOI: https://doi.org/10.62072/acm.2025.080305
ABSTRACT. This paper presents a new collection of trigonometric and inverse trigonometric integral formulas based on a known integral result. Some of these formulas evaluate to zero, while others are notable for their connection to well-known mathematical constants, such as π,√ 2, and the Catalan constant. Comprehensive proofs are provided for all results, and an open problem is posed to inspire further investigation.
Open AccessArticleOn Five Original Integral Inequalities of the Hardy-Hilbert Type
Christophe Chesneau*
Annals of Communications in Mathematics 2025,
8 (4),
431-441
DOI: https://doi.org/10.62072/acm.2025.080401
ABSTRACT.This article is devoted to five distinct integral inequalities of the Hardy-Hilbert type, each possessing its own originality. In particular, we highlight new trigonometric variants that yield sharp upper bounds involving weighted integral norms of the underlying functions. Complete and rigorous proofs are provided in detail.