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 ∈ ( 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.