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Journal of Applied Mathematics and Computation

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ArticleOpen Access http://dx.doi.org/10.26855/jamc.2026.09.001

Finest Bounds for the Sinc Trigonometric Function and Applications

Abd Raouf Chouikha

Université Paris-Sorbonne, Paris-Nord, Villetaneuse 93430, France.

*Corresponding author:Abd Raouf Chouikha

Published: August 06, 2026

Abstract

The function  has attracted significant attention from researchers due to its remarkable properties. It was introduced by Lord Rayleigh in his calculations involving Bessel functions. It is also related to the gamma function  as well as to Gauss’s  function. Furthermore, finding tighter bounds for such a function is a fascinating topic. In this paper, we prove for  the double inequality for the sinc function, 

with equality when r→0. Similar double inequalities are provided for the Huygens and the Wilker functions as well as for the Mitrinovic-Adamovic function. Consequently, we demonstrate that this bound, which depends on the parameter r, is sharper than those previously introduced by researchers.

Keyword

Trigonometric inequalities; Huygens inequalities; Wilker inequalities; Sinc function

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How to cite this paper

Finest Bounds for the Sinc Trigonometric Function and Applications

How to cite this paper: Abd Raouf Chouikha. (2026) Finest Bounds for the Sinc Trigonometric Function and Applications. Journal of Applied Mathematics and Computation10(3), 129-141.

DOI: http://dx.doi.org/10.26855/jamc.2026.09.001