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

Zhu, Ling

Comput. Math. Appl. 55, No. 11, 2498-2505 (2008).

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 \(0<|x|\leq\pi/2\).

MSC:

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

Keywords:

lower and upper bounds; A general form of Jordan’s inequality; Yang Le inequality; the spherical Bessel functions (SBFs); the SBFs of the first kind \(j_n (x) = \sqrt{\frac{\pi}{2x}}J_{n+\frac{1}{2}}(x)\); A new infinite series for \((\sin x)/x\)

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