Wilker and Huygens type inequalities for mixed trigonometric-hyperbolic functions
Yogesh J. Bagul, Ramkrishna M. Dhaigude, Barkat A. Bhayo, Vinay M., Raut
TL;DR
This paper establishes new Wilker and Huygens type inequalities involving mixed trigonometric and hyperbolic functions, providing bounds for sin(x)/x and tan(x)/x using hyperbolic functions.
Contribution
It introduces novel inequalities of Wilker and Huygens types for combined trigonometric-hyperbolic functions, extending previous work by Sándor.
Findings
New Wilker and Huygens inequalities involving mixed functions
Bounds for sin(x)/x and tan(x)/x in terms of hyperbolic functions
Extension of classical inequalities to combined trigonometric-hyperbolic context
Abstract
Motivated by the work of J. S\'andor [19], in this paper we establish a new Wilker type and Huygens type inequalities involving the trigonometric and hyperbolic functions. Moreover, in terms of hyperbolic functions, the upper and lower bounds of sin(x)/x and tan(x)/x are given.
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