New bounds of Sinc function by using a family of exponential functions

By using two–parameter functions in form of (a_0 + a_1 x + ⋯ a_n x^n)^α , this paper presents new bounds for approximating the Sinc function (sin x)/x , where the unknown a_i and α are determined with the help of two-points Páde approximation. Comparing with the bounds in previous literature, it achieves a much better approximation effect. A new method is also provided for proving the results.