A new method for sharpening the bounds of several special functions

DOI10.1007/s00025-017-0700-xzbMath1371.26020OpenAlexW2626264468MaRDI QIDQ2407011

Jiaer Shi, Xiao-Diao Chen, Yigang Wang, Pan Xiang

Publication date: 4 October 2017

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-017-0700-x

zbMATH Keywords

two-sided boundsexponential formJordan inequalityShafer-Fink inequality

Mathematics Subject Classification ID

Inequalities for trigonometric functions and polynomials (26D05) Inequalities involving other types of functions (26D07) Exponential and trigonometric functions (33B10)

Related Items (13)

Approximations to inverse tangent function ⋮ Improved bounds of Mitrinović-Adamović-type inequalities by using two-parameter functions ⋮ Monotonous two-parameter functions for asymptoticly approximating the inequalities involving the inverse tangent functions ⋮ New bounds of sinc function by using a family of exponential functions ⋮ Tighter bounds for the inequalities of sinc function based on reparameterization ⋮ A new method for proving some inequalities related to several special functions ⋮ New bounds of Wilker- and Huygens-type inequalities for inverse trigonometric functions ⋮ Some new results of Mitrinović-Cusa's and related inequalities based on the interpolation and approximation method ⋮ Some new bounds for Sinc function by simultaneous approximation of the base and exponential functions ⋮ Approximating trigonometric functions by using exponential inequalities ⋮ A family of Wilker's inequalities in two parameters and its applications ⋮ Generalizations and improvements of approximations of some analytic functions: a survey ⋮ New refinements and improvements of Jordan's inequality

Cites Work

• Sharpening of Jordan's type and Shafer-Fink's type inequalities with exponential approximations
• Sharp upper and lower bounds for a sine polynomial
• New strengthened Jordan's inequality and its applications
• A subtly analysis of Wilker inequality
• New approximations of some expressions involving trigonometric functions
• Inequalities for Lorentz polynomials
• Refinements of Jordan-Stečkin and Becker-Stark inequalities
• Sharpening Jordan's inequality and Yang Le inequality. II
• A new generalized and sharp version of Jordan's inequality and its applications to the improvement of the Yang Le inequality. II
• Sharpening Jordan's inequality and the Yang Le inequality
• Estimates for the arctangent function related to Shafer's inequality
• A new refined Jordan's inequality and its application
• SHARP BOUNDS FOR TRIGONOMETRIC POLYNOMIALS IN TWO VARIABLES
• Sharpening and generalizations of Shafer-Fink's double inequality for the arc sine function
• Sharpening of Jordan's inequalities and its applications
• Analytic Inequalities
• Sharpness and generalization of Jordan's inequality and its application
• Unnamed Item
• Unnamed Item

This page was built for publication: A new method for sharpening the bounds of several special functions