@article{Wang2024, 
author = {Suxia Wang and Tiehong Zhao},
title = {New refinements of Becker-Stark inequality},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {19677-19691},
keywords = {Becker-Stark inequality, power series, Gaussian hypergeometric function, monotonicity},
url = {https://www.sciopen.com/article/10.3934/math.2024960},
doi = {10.3934/math.2024960},
abstract = {This paper deals with the well-known Becker-Stark inequality. By using variable replacement from the viewpoint of hypergeometric functions, we provide a new and general refinement of Becker-Stark inequality. As a particular case, the double inequality                       π        2            −      (              π        2            −      8      )              sin        2            ⁡      x                      π        2            −      4              x        2              <            tan      ⁡      x        x    <                    π        2            −      (      4      −              π        2                    /            3      )              sin        2            ⁡      x                      π        2            −      4              x        2            for    x  ∈  (  0  ,  π      /    2  ) will be established. The importance of our result is not only to provide some refinements preserving the structure of Becker-Stark inequality but also that the method can be extended to the case of generalized trigonometric functions.}
}