New refinements of Becker-Stark inequality.

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 π² − (π² − 8) sin² x/π² − 4x² < tan x/x < π² − (4 − π²/3) sin² x/π² − 4x² 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. [ABSTRACT FROM AUTHOR]