A general refinement of Jordan-type inequality. (English) Zbl 1142.26317

Summary: A general form of Jordan’s inequality is established. The applications of this result give a general improvement of the Yang Le inequality and a new infinite series \((\sin x)/x=\sum_{n=0}^{\infty} a_n (\pi^2 -4x^2)^n\) for \(0<|x|\leq\pi/2\).


26D15 Inequalities for sums, series and integrals
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
Full Text: DOI


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