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Tighter bounds for the inequalities of Sinc function based on reparameterization

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this article, a new refined inequality containing trigonometric function for sinc function is established, which is based on the reparameterization technique. It utilizes the help of computer for proving the main results. It also provides two-sided bounds of \(\left( \frac{\sin (x)}{x}\right) ^\lambda \) for the cases that \(\lambda \in (1,4)\), which makes up for the leak that there is no two-sided bounds of \(\left( \frac{\sin (x)}{x}\right) ^\lambda \) for the cases that \(\lambda \in \left( \frac{7}{5},3-\frac{\pi }{2}\right) \). Numerical examples show that the new results achieves much tighter bounds than those of prevailing methods for sinc function.

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Acknowledgements

This research work was partially supported by Zhejiang Provincial Natural Science Foundation of China (LY19F020041), the National Science Foundation of China (61972120) and theNational Key R&D Program of China (2020YFB1708900) and TC190A4DA/3.

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Authors and Affiliations

  1. Key Laboratory of Complex Systems Modeling and Simulation, Hangzhou Dianzi University, Hangzhou, China

    Cheng Qian & Xiao-Diao Chen

  2. Department of Applied Mathematics, University of Belgrade, Belgrade, Serbia

    Branko Malesevic

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  1. Cheng Qian
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  2. Xiao-Diao Chen
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  3. Branko Malesevic
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Correspondence to Xiao-Diao Chen.

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Qian, C., Chen, XD. & Malesevic, B. Tighter bounds for the inequalities of Sinc function based on reparameterization. RACSAM 116, 29 (2022). https://doi.org/10.1007/s13398-021-01170-9

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