Series representations of the remainders in the expansions for certain trigonometric functions and some related inequalities, II

Chao-Ping Chen; Richard B. Paris

doi:10.1007/s13398-022-01208-6

Series representations of the remainders in the expansions for certain trigonometric functions and some related inequalities, II

Chao-Ping Chen^*, Richard B. Paris

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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Abstract

We examine Wilker and Huygens-type inequalities involving trigonometric functions making use of results derived in Part I. The Papenfuss–Bach inequality representing upper and lower bounds for the function x sec²x − tan x for 0 ≤ x < π/2 is also investigated. An open problem posed by Sun and Zhu concerning this last inequality is established.

Original language	English
Article number	62
Number of pages	20
Journal	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume	116
Issue number	2
Early online date	15 Jan 2022
DOIs	https://doi.org/10.1007/s13398-022-01208-6
Publication status	Published - 1 Apr 2022

Keywords

Wilker inequality
Huygens inequality
Papenfuss-Bach inequality
Trigonometric functions
Inequalities

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10.1007/s13398-022-01208-6

Paris_Series representations of the remainders_Accepted_2022Accepted author manuscript, 548 KB

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abstract = "We examine Wilker and Huygens-type inequalities involving trigonometric functions making use of results derived in Part I. The Papenfuss–Bach inequality representing upper and lower bounds for the function x sec2 x − tan x for 0 ≤ x < π/2 is also investigated. An open problem posed by Sun and Zhu concerning this last inequality is established.",

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Series representations of the remainders in the expansions for certain trigonometric functions and some related inequalities, II

Abstract

Keywords

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