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 journalArticlepeer-review

    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 sec− 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 languageEnglish
    Article number62
    Number of pages20
    JournalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
    Volume116
    Issue number2
    Early online date15 Jan 2022
    DOIs
    Publication statusPublished - 1 Apr 2022

    Keywords

    • Wilker inequality
    • Huygens inequality
    • Papenfuss-Bach inequality
    • Trigonometric functions
    • Inequalities

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