Tighter bounds for the inequalities of Sinc function based on reparameterization

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 sin ( x ) x λ for the cases that λ ∈ (...

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Bibliographic Details
Published inRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 116; no. 1
Main Authors Qian, Cheng, Chen, Xiao-Diao, Malesevic, Branko
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2022
Springer Nature B.V
Subjects
Applications of Mathematics
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
Trigonometric functions
Tighter bounds
Inequalities
Trigonometric function
33B10
Reparameterization
Sinc function
26D05
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Summary: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 sin ( x ) x λ for the cases that λ ∈ ( 1 , 4 ) , which makes up for the leak that there is no two-sided bounds of sin ( x ) x λ for the cases that λ ∈ 7 5 , 3 - π 2 . Numerical examples show that the new results achieves much tighter bounds than those of prevailing methods for sinc function.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-021-01170-9