A general refinement of Jordan-type inequality

DOI10.1016/j.camwa.2007.10.004zbMath1142.26317OpenAlexW2059324064MaRDI QIDQ945147

Ling Zhu

Publication date: 11 September 2008

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2007.10.004

zbMATH Keywords

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

Mathematics Subject Classification ID

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

Related Items (13)

Improvements of the bounds for Ramanujan constant function ⋮ Topics in Special Functions III ⋮ Inequalities for hyperbolic functions and their applications ⋮ The best approximation of the sinc function by a polynomial of degree \(n\) with the square norm ⋮ On Jordan type inequalities for hyperbolic functions ⋮ A note on Jordan type inequalities for hyperbolic functions ⋮ Unnamed Item ⋮ A general form of Jordan-type double inequality for the generalized and normalized Bessel functions ⋮ A source of inequalities for circular functions ⋮ Some new inequalities of the Huygens type ⋮ Jordan type inequalities involving the Bessel and modified Bessel functions ⋮ Sharpness and generalization of Jordan, Becker-Stark and Papenfuss inequalities with an application ⋮ Some new Wilker-type inequalities for circular and hyperbolic functions

Cites Work

• Generalized elliptic integrals and modular equations
• Inequalities for means
• New strengthened Jordan's inequality and its applications
• Spherical Bessel expansions of sine, cosine, and exponential integrals
• Sharpening Jordan's inequality and Yang Le inequality. II
• Evaluation of Fresnel integrals based on the continued fractions method
• Sharpening Jordan's inequality and the Yang Le inequality
• Analytic Inequalities
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A general refinement of Jordan-type inequality