A two-point-Padé-approximant-based method for bounding some trigonometric functions

DOI10.1186/s13660-018-1726-7zbMath1498.26026OpenAlexW2809015288WikidataQ55332354 ScholiaQ55332354MaRDI QIDQ824614

Jiapei Jin, Junyi Ma, Yigang Wang, Xiao-Diao Chen

Publication date: 15 December 2021

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-018-1726-7

zbMATH Keywords

two-sided boundsPadé approximanttrigonometric approximationWilker inequalityBecker-Stark inequality

Mathematics Subject Classification ID

Padé approximation (41A21) Inequalities for sums, series and integrals (26D15) Inequalities for trigonometric functions and polynomials (26D05) Exponential and trigonometric functions (33B10)

Related Items (7)

New bounds of sinc function by using a family of exponential 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 ⋮ Some new estimates of precision of Cusa-Huygens and Huygens approximations

Cites Work

• Unnamed Item
• Unnamed Item
• A refinement of the Becker-Stark inequalities
• Sharp Cusa type inequalities with two parameters and their applications
• Wilker and Huygens-type inequalities for the generalized trigonometric and for the generalized hyperbolic functions
• A subtly analysis of Wilker inequality
• Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities
• New approximations of some expressions involving trigonometric functions
• The natural algorithmic approach of mixed trigonometric-polynomial problems
• Refinements of Jordan-Stečkin and Becker-Stark inequalities
• Some notes on a method for proving inequalities by computer
• Sharpened versions of Mitrinović-Adamović, Lazarević and Wilkers inequalities for trigonometric and hyperbolic functions
• A method for proving some inequalities on mixed trigonometric polynomial functions
• A proof of two conjectures of Chao-Ping Chen for inverse trigonometric functions
• Several improvements of Mitrinovic-Adamovic and Lazarevics inequalities with applications to the sharpening of Wilker-type inequalities
• A further refinement of Wilker's inequality
• A proof of an open problem of Yusuke Nishizawa for a power-exponential function
• Series representations of the remainders in the expansions for certain trigonometric functions and some related inequalities, I
• Some improvements of Jordan-Steckin and Becker-Stark inequalities
• The natural approach of Wilker-Cusa-Huygens inequalities

This page was built for publication: A two-point-Padé-approximant-based method for bounding some trigonometric functions